SAT Problem-Solving and Data Analysis practice questions
Ratios, percentages, probability and reading data from tables and graphs — heavy on careful interpretation.
675 free questions, each with a full worked solution and an explanation of what each wrong answer means.
Practise this domain adaptively →Easy (133)
- Percent of a quantity
What is 40% of 150? - Percent of a quantity
A class has 25 students, and 60% of them play a sport. How many students play a sport? - Unit conversion
A runner covers 3 kilometers. Given that 1 kilometer equals 1000 meters, how many meters is this? - Range of a data set
What is the range of the number of hours worked by these 6 volunteers? - Percent increase applied to a price (sales tax)
A shirt has a price of $24.00. A sales tax of 8% of the price is added to the price. What is the total cost, in dollars,… - Probability from a two-way frequency table
If one of these 80 students is selected at random, what is the probability that the student chose Music? - Proportional reasoning with a scale
On a map, a distance of 1 inch represents an actual distance of 12 miles. Two towns are 4.5 inches apart on this map. Wh… - Interpreting a margin of error
Which statement is best supported by these results? - Association versus causation in an observational study
Which conclusion is best supported by this study? - Interpreting the slope of a line of best fit
What does the number 2.5 most likely represent? - Scaling a ratio
In a bag of marbles, the ratio of red marbles to blue marbles is 3 to 5. If there are 24 red marbles, how many blue marb… - Mean of a data set
What is the mean of the data set 4, 8, 9, 15? - Simple probability
A bag contains 3 red marbles and 5 blue marbles. If one marble is chosen at random, what is the probability that it is r… - Estimating a population count from a sample
A quality inspector randomly selects 80 light bulbs from a shipment of 5,000 and finds that 4 of them are defective. Bas… - Probability from equally likely outcomes
A spinner has 8 equal sections numbered 1 through 8. What is the probability that a single spin lands on a number greate… - Unit rate: miles per gallon
A car uses 6 gallons of fuel to travel 180 miles. At this rate, how many miles does the car travel per gallon? - What percent one number is of another
What percent of 80 is 20? - Probability with a die
A fair six-sided die, numbered 1 through 6, is rolled once. What is the probability that the number rolled is less than … - Complement of an event
The probability that a spinner lands on blue is 3/8. What is the probability that the spinner does NOT land on blue? - Median of an unordered list
Seven runners recorded the following times, in minutes, for a race: 33, 29, 41, 37, 30, 45, 36. What is the median time,… - Percent of a count
A jar holds 60 sweets, and 15% of them are red. How many red sweets are in the jar? - Probability from a spinner with repeated colours
A spinner is divided into three equal sections: two are red and one is blue. What is the probability that the spinner la… - Hours to minutes
How many minutes are there in 3.5 hours? - Mode of a short list
The shoe sizes sold by a shop during one hour were 7, 8, 8, 9, 10, 8, 7. What is the mode of these sizes? - Simplest form of a ratio
In a class, the ratio of boys to girls is 18 : 24. What is this ratio in simplest form? - Probability from letters of a word
One letter is chosen at random from the six letters of the word BANANA. What is the probability that the letter chosen i… - Minutes to seconds
How many seconds are there in 1.5 minutes? - Probability from a drawer of socks
A drawer contains 4 black socks and 6 white socks. If one sock is taken out at random, what is the probability that it i… - Cost per egg
A dozen eggs costs $3.60. What is the cost of one egg, in cents? - Mean points per game
A basketball player scored 12, 18 and 24 points in three games. What was the player's mean number of points per game? - Probability from a bag of sweets
A bag holds 20 sweets, 5 of which are red. If one sweet is picked at random, what is the probability that it is red? - Kilograms to grams
How many grams are there in 3 kilograms? - Probability from a spinner
A spinner is divided into 12 equal sections, 3 of which are red. If the spinner is spun once, what is the probability th… - Scaling a simple rate
A recipe uses 3 eggs to make 12 pancakes. How many eggs are needed to make 48 pancakes? - Percent of a group in context
A class of 80 pupils voted on an activity for sports day, and 25% of them chose swimming. How many pupils chose swimming… - Ten percent of an amount
A jacket costs $250. What is 10% of its price, in dollars? - Increasing a number by a percent
A plant was 60 centimetres tall and then grew by 50%. How tall is it now, in centimetres? - Writing a fraction as a percent
In a class of 60 pupils, 15 walk to school. What percent of the class walks to school? - Price after a percent discount
A game costs $40 and is on sale at 20% off. What is the sale price, in dollars? - Mean of four numbers
What is the mean (average) of the numbers 4, 8, 6, and 2? - Median of five numbers
What is the median of the numbers 3, 9, 5, 7, and 1? - Mode of a data set
What is the mode of the data set 2, 5, 5, 8, 5, 3? - Range of heights in context
In a class, the tallest pupil is 165 centimetres tall and the shortest is 140 centimetres tall. What is the range of the… - Total from a mean and a count
The mean of three numbers is 20. What is the sum of the three numbers? - Direction of a relationship in a scatterplot
A scatterplot shows the hours pupils spent revising and their test scores. The points rise from the lower left to the up… - Prediction from a line of best fit
A line of best fit for a scatterplot is y = 2x + 10. What value of y does the line predict when x = 5? - Reading a two-way table
A survey of 50 pupils recorded whether each has a pet and whether each plays a sport. | Plays a sport | Does not play … - Estimating a population count from a sample proportion
In a random sample of 100 pupils from a school of 500, 60 said they prefer football. Based on the sample, about how many… - Recognising a random sample
A head teacher wants a random sample of 20 pupils from the school. Which method gives a random sample? - Interval from an estimate and a margin of error
A poll estimates that 45% of a town's residents support a new park, with a margin of error of 3 percentage points. Which… - Effect of sample size on the margin of error
A survey is repeated with a much larger random sample. What happens to the margin of error? - Identifying the population in a survey
A researcher surveys 50 randomly chosen residents of a town of 5,000 people about recycling. What is the population in t… - Best estimate of a population mean
A random sample of 40 apples from an orchard has a mean mass of 150 grams. What is the best estimate, in grams, of the m… - Sample proportion
In a survey of 200 shoppers, 50 said they had bought bread that day. What fraction of the sample bought bread? - Count from a sample percentage
In a random sample of 400 voters, 30% said they would vote for the new library. How many of the 400 voters said this? - Slope of a line of best fit as a rate
A line of best fit for a scatterplot has a slope of 3. According to the line, when x increases by 1, by how much does th… - Naming a negative association
A scatterplot of hours spent watching television against test score shows that pupils who watched more television tended… - Completing a simple two-way count
A class of 40 pupils was asked whether they like cats. 25 said yes. How many said no? - Interpreting a point on a scatterplot
A scatterplot shows, for each pupil in a class, the number of books read in a term (x-axis) and the pupil's reading test… - Reading a two-way table row
In a survey, 30 people said they walk to work. Of those 30, 12 own a dog. How many of the people who walk to work do not… - Meaning of the y-intercept of a line of best fit
A line of best fit for a scatterplot is y = 0.5x + 20. What does the number 20 represent? - Why a tiny sample cannot support a claim about a town
Ella asked 10 of her friends whether they like pizza, and 8 said yes. She concludes that 80% of the people in her town l… - Recognising a biased sample in an advert
An advert says '9 out of 10 dentists recommend our toothpaste.' The 10 dentists asked all work for the company that make… - Correlation from a shared cause
In a seaside town, ice cream sales and cases of sunburn both rise every summer. Which conclusion is justified? - Association is not proof of cause
A study found that pupils who eat breakfast tend to score higher on tests than pupils who do not. Which conclusion is ju… - Reading 'up to' in a claim
A shop sign says 'Up to 50% off everything.' Which statement is true? - A mean that rises while most values fall
In a town, the average (mean) house price rose last year, yet most houses sold for less than the year before. Which expl… - Sample that does not represent a town
A researcher stands outside a gym and asks people leaving it whether they exercise every week. 90% say yes. Why can the … - What a mean hides
A school reports that the mean score on a test was 70. A parent concludes that every pupil scored about 70. What is wron… - A graph that exaggerates a change
A bar chart shows sales rising from 100 to 104, but the bars look very different in height. Which feature of the chart m… - Scaling a recipe
A recipe for 4 people uses 200 grams of rice. How many grams of rice are needed for 6 people? - Pages per minute
A printer prints 90 pages in 3 minutes at a steady rate. How many pages does it print per minute? - Discount amount from a percentage
A shop takes 15% off the price of an $80 coat. How many dollars is the discount? - Percentage absent
In a class of 25 pupils, 5 are absent today. What percentage of the class is absent? - Mode of a small data set
The ages of five children are 4, 7, 7, 9, and 13. What is the mode of the ages? - Mean of three scores
Three friends scored 12, 15, and 18 in a quiz. What was their mean score? - Direction of an association
A scatterplot shows that on days with higher temperatures, a café sells more iced drinks. Which of the following best de… - Extending a table pattern
The table shows the score a student earned for different numbers of hours studied. Hours | Score 1 | 50 2 | 60 3 | 70 … - Probability of drawing a high card
A box holds 10 cards numbered 1 to 10. One card is drawn at random. What is the probability that the number on the card … - Probability of the complement
The probability that it rains tomorrow is 0.3. What is the probability that it does not rain tomorrow? - Choosing a representative sample
A researcher wants to estimate the mean height of all 1,200 pupils at a school. Which of the following samples would giv… - What a random sample supports
A random sample of 500 adults in a city was surveyed, and 40% of them said they cycle at least once a week. Which of the… - Spotting a biased sample
A store asked customers as they left the store with their shopping whether they liked the store, and 95% said yes. The s… - Association is not causation
In a town, both ice cream sales and the number of sunburn cases rise during the summer. Which of the following statement… - Distance at a steady speed
A car travels 60 kilometres in 1 hour. At the same speed, how many kilometres does it travel in 4 hours? - Pupils absent from a class
A class has 30 pupils, and 10% of them are absent today. How many pupils are absent? - Median shoe size
The shoe sizes of five children are 1, 3, 2, 5, and 4. What is the median shoe size? - Recognising no association
A scatterplot shows the shoe sizes of 40 pupils against their reading test scores. The points are scattered with no visi… - Probability a random day starts with T
One of the seven days of the week is chosen at random. What is the probability that its name begins with the letter T? - Estimating from a random sample of apples
In a random sample of 50 apples picked from an orchard's 5,000 apples, 4 had worms. About how many of the orchard's appl… - A claim based on the shop's own staff
A bakery's sign reads: "Our bread is the best in town: 9 out of 10 of our bakers agree." Which of the following is the b… - Cost per battery in a pack
A pack of 8 batteries costs $10. What is the cost of one battery, in dollars? - Percent of sweets that are not red
A bag holds 20 sweets, and 15 of them are red. What percent of the sweets are not red? - Range of race times
A runner's times in five races were 21, 19, 23, 20, and 22 minutes. What is the range of these times, in minutes? - Describing a rising-together association
Over a summer, a town's weekly ice cream sales and its weekly count of sunburn cases were recorded. Weeks with higher ic… - Probability a month starts with J
One of the 12 months of the year is chosen at random. What is the probability that its name begins with the letter J? - Flow rate of a tap
A tap fills a 30-litre bucket in 5 minutes. At that rate, how many litres flow from the tap each minute? - Grams of salt in a tin
A 400-gram tin of beans contains 5% salt by mass. How many grams of salt are in the tin? - Mean mass of one egg
A box of 6 eggs has a total mass of 360 grams. What is the mean mass of one egg, in grams? - Choosing a representative sample
A school wants to estimate what fraction of its 900 students walk to school. Which sample would give the most reliable e… - Estimating a school total from a random sample
In a random sample of 150 students from a school of 900, 30 said they cycle to school. Based on the sample, about how ma… - Generalising from a survey at one place
A survey of 200 people leaving a gym found that 85% exercise at least three times a week. To which group can this result… - Recognising a misleading average
A company reports that the average salary of its 10 employees is $90,000. Nine of the employees earn $40,000 each and th… - Reading a trend from paired data
A table shows that as the number of hours a shop stays open each day increased from 6 to 8 to 10, its daily sales rose f… - Probability of picking a weekend day
One of the seven days of the week is chosen at random. What is the probability that the chosen day is a Saturday or a Su… - Bread rolls per person
A basket of 12 bread rolls is shared equally among 3 people. How many rolls does each person get? - Half of a class as a percent
A class has 40 pupils. 50% of them walk to school. How many pupils walk to school? - Range of four temperatures
Four days' high temperatures were 12°, 7°, 15°, and 9°. What is the range of these temperatures, in degrees? - Reading a decreasing relationship
As the price of a cinema ticket rose from $5 to $7 to $9, the number of tickets sold each week fell from 800 to 600 to 4… - Probability of drawing a numbered ticket
Ten raffle tickets numbered 1 to 10 are in a hat, and one is drawn at random. What is the probability that the number dr… - Choosing the population an estimate applies to
A researcher surveys a random sample of 400 students at one university and finds that 30% have a part-time job. To which… - Speed of a walker
A walker covers 60 kilometres in 4 days, walking the same distance each day. How many kilometres does the walker cover e… - Discount in dollars
A coat priced at $200 is reduced by 30%. By how many dollars is the price reduced? - Spotting an outlier
A data set is 3, 4, 4, 5, 40. Which value is an outlier? - Choosing the group a survey represents
A survey of 300 shoppers leaving a toy store asks how much they spent on toys last month. The results can most reasonabl… - Yearly change from a line of best fit
For a set of used cars, the value y, in dollars, is modelled by y = 20,000 − 1,500x, where x is the car's age in years. … - Probability of not walking to school
Of the 25 pupils in a class, 10 walk to school. If one pupil is chosen at random, what is the probability that the pupil… - Conclusion from a random sample of shoppers
In a random sample of 50 shoppers at a store, 30 said they preferred the store's new packaging. Which of the following i… - Why a park survey may not represent the town
A survey about a town's new park was given only to people using the park on a Saturday afternoon. Which of the following… - Eggs for a larger batch
A recipe uses 3 eggs for every 2 cups of flour. How many eggs are needed for 8 cups of flour? - Percentage of a class wearing glasses
In a class of 25 pupils, 8 wear glasses. What percent of the class wears glasses? - Pages printed in five minutes
A printer prints 24 pages per minute. How many pages does it print in 5 minutes? - Number of left-handed pupils
In a class of 40 pupils, 25 percent are left-handed. How many pupils are left-handed? - Counting values in a dot plot
A dot plot shows three dots above 2, one dot above 3, and two dots above 4. How many data values does the plot represent… - Predicted score from a model
A model for a class relates hours studied x to test score y by y = 5x + 50. What score does the model predict for a stud… - Probability of winning a raffle
Of the 50 tickets in a raffle, Amira bought 4. If one winning ticket is drawn at random, what is the probability that Am… - Estimating bruised apples in a crate
A random sample of 50 apples from a crate of 500 apples contains 4 bruised apples. Based on the sample, what is the best… - Flaw in generalising from a basketball team
A study measured the heights of the players on a school's basketball team and concluded that pupils at the school are un… - People with at least one pet
A survey asked 20 people how many pets they have. Eight people have none, seven have one, and five have two. How many of… - Meaning of a constant in a draining model
The equation y = 40 − 2x models the number of litres y of water left in a tank x hours after it starts draining. What do… - Probability of drawing a king
A pile of 10 cards contains 3 kings. If one card is drawn at random, what is the probability that it is a king? - Why samples are used
A researcher wants to know the average commuting time of the 200,000 workers in a city. Which of the following is the be… - Weakness of an advertisement's claim
An advertisement says that 9 out of 10 users of a diet product lost weight. The claim is based on 10 people chosen by th…
Easy–Medium (133)
- Percentages
A jacket originally priced at $80 is discounted by 25%. What is the sale price? - Simple probability
A bag contains 3 red, 5 blue, and 2 green marbles. If one marble is drawn at random, what is the probability it is red? - Proportional reasoning
A recipe uses 2 cups of flour to make 3 servings. How many cups of flour are needed for 12 servings? - Median
What is the median of the data set 4, 7, 7, 9, 13? - Ratios
The ratio of dogs to cats at a shelter is 5 to 3. If there are 40 dogs, how many cats are there? - Rates and unit rate
A printer produces 8 pages every 5 seconds. At this rate, how many pages does it produce in 1 minute? - Effect of sample size on margin of error
Compared with the first survey, the margin of error for the second survey will most likely be - What a random sample allows you to generalise to
Which conclusion is most appropriate? - Predicting from a line of best fit
According to the model, what is the predicted value of y when x = 15? - Converting units
A trail is 3.5 kilometres long. What is the length of the trail in metres? (1 kilometre = 1,000 metres) - What percent one number is of another
A class has 80 students, and 12 of them walk to school. What percent of the students in the class walk to school? - Conditional probability from a two-way table
If a senior is chosen at random, what is the probability that the senior has a driver's licence? - Unit price
A 5-kilogram bag of rice costs $12.50. What is the cost per kilogram? - Price after a percent discount
A jacket that normally costs $48 is on sale at 25% off. What is the sale price? - Range of a data set
What is the range of the data set 15, 22, 9, 30, 18? - Spotting a biased sample
A newspaper reports: 'A survey of 2,000 visitors to a ski resort found that 85% of them enjoy winter, so most people in … - Interpreting the y-intercept of a model
The line of best fit for a scatterplot of a taxi's fare, y, in dollars, against the distance travelled, x, in miles, is … - Enlarging a photo in proportion
A photograph is 4 inches wide and 6 inches tall. It is enlarged so that its proportions stay the same and its width beco… - The population a random sample can speak for
A survey of 200 students selected at random from all students at Northfield High School found that 45% of them walk to s… - Probability of 'not' an outcome
A bag contains 4 red marbles, 6 blue marbles and 10 green marbles. If one marble is drawn at random, what is the probabi… - Values inside a margin of error
A random sample of 500 households in a region found that 38% of them own a pet, with a margin of error of 4 percentage p… - What a margin of error means
A poll of randomly selected adults reports that 47% support a proposal, with a margin of error of 3 percentage points. W… - Equation matching a table
Which equation describes the relationship between x and y shown in the table? - Mean versus median with an outlier
For the data set 2, 3, 4, 5, 26, which statement is true? - Amount of a discount
A coat priced at $60 is marked 30% off. What is the amount of the discount, in dollars? - Spotting a leading question
A town council wants an unbiased estimate of residents' views on a proposed stadium. Which survey question is most likel… - Describing an association from a scatterplot
In a scatterplot, the points lie close to a straight line that slopes downward from left to right. Which of the followin… - Count from a probability
A bag contains 30 marbles, each either red or blue. The probability of drawing a red marble at random is 2/5. How many b… - Reading a scale drawing
On a scale drawing, 2 centimetres represent 5 metres. A wall measures 7 centimetres on the drawing. How long is the actu… - Margin of error from an interval
A poll based on a random sample reports that support for a proposal is between 45% and 51%, at a 95% confidence level. W… - Scatterplot showing no association
Which of the following descriptions of a scatterplot indicates NO association between the two variables? - Either of two events that cannot both happen
On a given day, the probability of rain is 0.3 and the probability of snow is 0.1, and it cannot both rain and snow on t… - Percent of the remainder
In a survey of 120 people, 48 answered yes to a question and everyone else answered no. What percent of the people surve… - Non-response as a source of bias
A council mailed a survey about a proposed car park to all 2,000 households in a district. Only 300 replied, and most of… - Extending a table of a linear function
The table shows values of a linear function g. What is the value of g(5)? - Adding a constant to every value
A data set has a mean of 12. If 5 is added to every value in the data set, what is the mean of the new data set? - Recognising a self-selected sample
Which of the following is an example of a self-selected sample? - A line of best fit with slope zero
The line of best fit for a scatterplot has a slope of 0. Which of the following best describes the relationship shown by… - Finding the whole from a percent
20% of a number is 35. What is the number? - What a sample percentage is
A poll of 800 randomly selected voters in a city found that 62% of them support a new park. Which of the following best … - Constant of proportionality from a table
The values in the table satisfy y = kx for some constant k. What is the value of k? - Percent increase in a price
A bicycle that cost $80 last year costs $100 this year. By what percent did its price increase? - Recognising an observational study
Which of the following describes an OBSERVATIONAL study rather than an experiment? - Intercept of a fitted line from its slope and a point
The line of best fit for a scatterplot has a slope of 2 and passes through the point (3, 11). What is the y-intercept of… - Range after adding a value
The data set 3, 9, 4, 7 has the value 12 added to it. What is the range of the new data set? - Sample estimate from an interval
A survey based on a random sample reports that a plausible range for the mean weekly grocery spending of all households … - Predicted change from a slope
The line of best fit for a set of data is y = 3x + 2. According to the line, if x increases by 4, by how much does the p… - Number correct from a percent
A test has 40 questions. A student answered 85% of them correctly. How many questions did the student answer correctly? - Interval from an estimate and a margin
A poll of randomly selected voters estimates that 40% support a candidate, with a margin of error of 3 percentage points… - Pair of variables with a negative association
The line of best fit for a scatterplot has a NEGATIVE slope. Which of the following pairs of variables is most likely to… - Median of an even number of values
The numbers of emails a person received on six days were 8, 3, 5, 9, 2 and 7. What is the median number of emails? - Which statistic equals 7
The data set shows the number of goals scored by a football team in each of seven matches: 4, 4, 5, 6, 7, 9, 14. Which o… - Part from a ratio and a total
A paint mixture uses blue and white in the ratio 5 to 3. How many millilitres of blue are needed to make 120 millilitres… - Scaling a sample proportion to a population
In a random sample of 250 students at a university of 5,000 students, 32% said they commute by bicycle. Based on the sam… - Spotting a biased sampling method
A school newspaper wants to estimate the proportion of all students at the school who play a musical instrument. Which s… - Probability of not drawing a colour
A bag contains 20 marbles: 8 red, 6 blue, and 6 green. If one marble is drawn at random, what is the probability that it… - Range of a data set
The number of emails a worker received on each of nine days was 3, 5, 5, 6, 8, 8, 8, 9, and 12. What is the range of the… - Percent of a total that a part represents
A jar holds 30 sweets, of which 24 are wrapped. What percent of the sweets are wrapped? - Interval from an estimate and margin
A random sample of a hotel's guests gives an estimated mean stay of 6.2 nights with a margin of error of 0.4 nights. Whi… - Probability of one event or another
A box holds 8 cards numbered 1 through 8. One card is drawn at random. What is the probability that the number is either… - Percent remaining after a percent used
A gardener had 45 litres of fertiliser and used 40% of it in spring. How many litres remained? - Scaling a recipe
A recipe that serves 2 people uses 7 tablespoons of oil. How many tablespoons of oil are needed to serve 6 people? - Sample size and reliability
Two surveys estimate the proportion of a town's residents who use the library. Survey 1 asked 50 randomly chosen residen… - Probability of two independent events
A fair six-sided die is rolled twice. What is the probability that both rolls show a 6? - Identifying the mode
The ages of eight members of a hiking group are 12, 15, 15, 18, 20, 20, 20, and 24. What is the mode of the ages? - Unit rate then scaling
A printer prints 500 pages in 8 minutes at a constant rate. How many pages does it print in 3 minutes? - Which sampling method gives an unbiased estimate
A city wants to estimate the proportion of its residents who own a car. Which sampling method is most likely to produce … - Probability of drawing a specific rank
A standard deck has 52 cards, 4 of which are aces. If one card is drawn at random, what is the probability that it is an… - Proportion in a mixture
A fruit punch is made by mixing juice and soda in the ratio 3 : 1. How many litres of juice are in 20 litres of punch? - Estimating a population count from a sample
In a random sample of 300 households in a town of 8,000 households, 90 have a dog. What is the best estimate of the numb… - Identifying a leading question
A council surveys residents about a proposed car park. Which of the following questions is most likely to bias the respo… - Scaling a sample proportion to a population
A random sample of 150 pupils at a school of 2,400 pupils finds that 45 walk to school. What is the best estimate of the… - Recognising a biased question
A school surveys pupils about a proposal to shorten the lunch break. Which question is most likely to bias the responses… - Scaling a ratio of ingredients
A recipe uses flour and sugar in the ratio 3 : 2 by mass. How many grams of sugar are needed with 450 grams of flour? - Distance from a fuel rate
A car travels 210 kilometres on 15 litres of fuel. At the same rate, how far, in kilometres, can it travel on 24 litres? - Mean minus median of a small data set
For the data set 4, 7, 7, 9, 13, what is the mean minus the median? - Probability from a spinner with unequal groups
A spinner has 12 equal sections: 3 are red, 4 are blue, and the rest are green. What is the probability that one spin la… - Sale price after a percent reduction
A jacket priced at $50 is reduced by 30%. What is the sale price, in dollars? - Percentage of pupils who walk
Of the 40 pupils in a class, 18 walk to school. What percentage of the class walks to school? - Median house price
Five houses on a street sold for $210,000, $180,000, $250,000, $190,000, and $220,000. What was the median price, in tho… - Range of daily sales
A shop's sales on five days were $120, $95, $140, $160, and $85. What is the range of these sales, in dollars? - Interpreting a downward trend
A scatterplot shows the age of used cars on the x-axis and their selling prices on the y-axis. The points trend downward… - Probability of a high roll
A fair six-sided die is rolled once. What is the probability that the result is greater than 4? - Probability of not wearing glasses
In a class of 30 pupils, 12 wear glasses. A pupil is chosen at random. What is the probability that the pupil does not w… - Why one year group is a poor sample
A school wants to estimate the average time its 800 pupils spend on homework each night. It surveys every pupil in the o… - Kilometres per litre
A car travels 240 kilometres on 20 litres of fuel. How many kilometres does it travel per litre? - A claim from a tiny sample
A café asked 10 customers to try a new flavour of ice cream, and 8 said they liked it. The café then advertised: "80% of… - Percent increase in a price
The price of a ticket rose from $40 to $50. By what percent did the price increase? - Fifth value from a known mean
A data set has five values and a mean of 10. Four of the values are 8, 9, 11, and 12. What is the fifth value? - Spotting an outlier on a scatterplot
On a scatterplot, all but one of the points lie close to the line y = x. Which of the following points is most likely th… - Probability of not picking green
A jar holds 5 green sweets and 15 yellow sweets. One sweet is taken at random. What is the probability that it is not gr… - Plausible range from an estimate with uncertainty
A poll of a random sample of voters estimates that 60% support a new park, give or take 4 percentage points. Which of th… - Balls of wool for a longer scarf
A knitting pattern uses 3 balls of wool for a scarf 120 centimetres long. At the same rate, how many balls of wool are n… - Minutes to print a document
A printer prints 12 pages per minute. How many minutes does it take to print a 90-page document? - Tank capacity from a percentage full
A tank is 35% full and holds 140 litres of water. What is the capacity of the tank, in litres? - Percent of seeds that sprouted
Of 250 seeds planted, 210 sprouted. What percent of the seeds sprouted? - Mode from a frequency description
In a quiz, 3 students scored 6 points, 5 students scored 7 points, and 2 students scored 8 points. What is the mode of t… - Model from a table of plant heights
A plant's height was recorded each week: 4 cm at week 0, 7 cm at week 1, 10 cm at week 2, and 13 cm at week 3. Which equ… - Probability of drawing a multiple of 8
A box holds 40 cards numbered 1 through 40. One card is drawn at random. What is the probability that the number on the … - Estimating a school total from a sample
In a random sample of 80 students from a school of 1,200 students, 12 said they walk to school. Based on the sample, wha… - Why an online poll cannot be generalised
A poll posted on a cycling club's website found that 90% of respondents support building new bike lanes in the city. Whi… - Currency conversion
On a certain day, 1 US dollar could be exchanged for 0.92 euros. How many euros could be obtained for 250 US dollars at … - Trees that survived
Of 1,250 trees planted along a road, 8% died in the first year. How many of the trees survived the first year? - Total from a mean
The mean mass of 5 parcels is 4.2 kilograms. What is the total mass of the 5 parcels, in kilograms? - Meaning of the slope in a study-time model
A model based on a scatterplot predicts a student's test score s from the number of hours h spent studying: s = 12h + 20… - Probability a spinner does not land on green
A spinner has 5 equal sections: two are red, one is blue, and two are green. What is the probability that a single spin … - Estimating defective bulbs in a batch
A random sample of 120 light bulbs is taken from a batch of 6,000, and 3 of the sampled bulbs are found to be defective.… - Flaw in a self-selected phone-in poll
A radio station asks listeners to phone in to say whether they support a new tax. Of 1,200 callers, 70% oppose it. Which… - Sugar for a larger batch of jam
A jam recipe uses 5 kilograms of sugar for every 2 kilograms of fruit. How many kilograms of sugar are needed for 6 kilo… - Price after a discount
A pair of shoes priced at $60 is sold at 15% off. What is the sale price, in dollars? - Mean of five quiz scores
A student's five quiz scores are 7, 9, 4, 9, and 6. What is the mean score? - Meaning of the intercept in a rental model
A model gives the cost C, in dollars, of renting a hall for h hours as C = 40h + 150. What does the number 150 represent… - Probability of drawing a green counter
A bag holds 4 green, 6 yellow, and 2 white counters. One counter is drawn at random. What is the probability that it is … - Estimating a population from a random sample
In a random sample of 60 residents of a town of 2,000, 18 said they had visited the new library. Based on the sample, ab… - Recognising a biased sample
To estimate how many households in a town own a dog, a researcher surveys 100 people at a dog show. Which statement best… - Fertiliser for a larger lawn
A gardener uses 4 kilograms of fertiliser for every 10 square metres of lawn. How many kilograms are needed for 25 squar… - Number of pupils who cycle
A school has 80 pupils in Year 6, and 35% of them cycle to school. How many Year 6 pupils cycle to school? - Difference between the mean and the median
For the data set 4, 8, 8, 12, 18, by how much does the mean exceed the median? - Describing the association in a scatterplot
A scatterplot shows the age of each of 30 used cars and its sale price. Older cars tend to have lower prices. Which of t… - Probability of drawing an even-numbered card
Nine cards numbered 1 to 9 are shuffled, and one is drawn at random. What is the probability that the card shows an even… - Estimating from a random sample of a village
In a random sample of 45 households in a village of 1,500 households, 9 keep chickens. Based on the sample, about how ma… - Spotting a sample that is not representative
To estimate the average number of books read per year by adults in a city, a researcher surveys 200 people leaving the c… - Effect of one larger value on mean and median
The heights, in centimetres, of five plants are 12, 15, 15, 18, and 20. If the tallest plant were 30 centimetres instead… - Probability of not drawing green
A bag contains 4 red, 3 blue and 5 green marbles. One marble is drawn at random. What is the probability that it is not … - Estimating support from a sample
In a random sample of 200 voters in a town, 120 support a new measure. Based on the sample, what is the best estimate of… - Why a phone-in vote is not a fair sample
A radio station asks its listeners to phone in and vote on whether the station plays good music. Of those who phoned, 95… - Percent of questions answered correctly
A test has 40 questions, and Leo answered 34 of them correctly. What percent of the questions did Leo answer correctly? - Interpreting the slope of a model
The model y = 2.5x + 10 relates x, hours of practice per week, to y, points scored in a game. Which of the following is … - Probability of choosing a prime
A whole number from 1 to 20 is chosen at random. What is the probability that the number is prime? - Choosing a representative sample of pupils
A researcher wants a sample of 80 pupils that represents all 800 pupils at a school. Which method is most likely to give… - Why five friends cannot stand for everyone
A student asks five friends whether they prefer tea or coffee, and all five say tea. The student concludes that most peo… - Effect of adding a constant on the range
Five test scores are 70, 75, 80, 85, and 90. If 5 points are added to every score, what happens to the range of the scor… - Equation fitting a table of pairs
A table gives the pairs (0, 5), (1, 7), (2, 9), and (3, 11). Which equation fits all four pairs?
Medium (141)
- Ratios and rates
A car travels 150 miles in 2.5 hours. At this rate, how far will it travel in 4 hours? - Percent change
The price of a stock rises from $40 to $50. What is the percent increase? - Line of best fit
Based on the model, what score does the line predict for a student who studies 5 hours? - Percent change
A population decreases from 250 to 200 over a year. What is the percent decrease? - Two-way tables
If one person is chosen at random from those who prefer tea, what is the probability the person is under 30? - Statistics: mean, median, range
What is the difference between the mean and the median of this data set? - Density / rate as a unit rate
A machine fills 3 bottles every 4 seconds. How many seconds does it take to fill 27 bottles? - Choosing a change that reduces margin of error
Which change would be most likely to decrease the margin of error, assuming all other aspects of the survey are unchange… - What random assignment licenses
Which conclusion is best supported? - Comparing an observed value with a predicted value
Which statement best describes this data point? - Choosing between a linear and an exponential model
Which type of model best fits these data, and why? - Constant rate over a new time
A train travels 180 miles in 3 hours at a constant speed. At the same speed, how many miles does it travel in 7.5 hours? - Finding the original price after a percent increase
The price of a jacket was increased by 20%, and the new price is $72. What was the original price, in dollars? - Median of an unordered data set with an even count
A soccer team scored 2, 5, 1, 3, 4, and 5 goals in its six matches this season. What is the median number of goals score… - Effect of an outlier on the mean and median
A data set consists of the ages of 20 people. Nineteen of them are between 30 and 35 years old, and one is 90 years old.… - Probability of the complement
The probability that a certain flight departs on time is 0.35. What is the probability that the flight does NOT depart o… - Map scale
On a map, 1 centimetre represents 25 kilometres. Two towns are 6.4 centimetres apart on the map. What is the actual dist… - Mode of a data set
The number of books read by each of eight students over the summer was 2, 9, 9, 4, 6, 9, 4 and 13. What is the mode of t… - Probability of two independent events
A fair coin is flipped twice. What is the probability that both flips land heads? - Prediction from a line of best fit
For a group of students, the line of best fit relating hours of television watched per week, x, to score on a quiz, y, i… - Interpreting a poll's margin of error
A poll of 1,000 randomly selected voters found that 52% support a ballot measure, with a margin of error of 3 percentage… - Upper end of a plausible interval
A random sample of 150 loaves from a bakery has a mean mass of 812 grams, and the associated margin of error is 9 grams.… - Random selection without random assignment
Researchers selected 1,000 adults at random from a country's population and recorded each adult's diet and blood pressur… - Solving a model for the input
A model predicts a shop's monthly profit, y, in dollars, from its monthly advertising spend, x, in dollars: y = 4x + 200… - Median from a frequency table
What is the median number of siblings for the 20 students? - Percent of a percent
In a survey, 60% of the respondents own a car, and 25% of those car owners own an electric car. What percent of all the … - Converting a rate across time units
Water flows from a pipe at a constant rate of 2.5 litres per second. How many litres flow from the pipe in 1 hour? - Choosing a representative sample
A principal wants to estimate the percent of the 1,200 students at her school who cycle to school. Which of the followin… - Computing a residual
For a set of data, the line of best fit is y = 3x + 5. One data point in the set has coordinates (4, 20). What is the di… - Conditional probability from group counts
A café recorded the orders of 120 customers one morning: 70 ordered coffee and 50 ordered tea. Of the coffee drinkers, 4… - Mean from a frequency list
What is the mean number of books read per student? - Which design supports a causal conclusion
Four studies each compared weight change between people on two diets. In which study could a conclusion that one diet CA… - Recognising exponential growth
A quantity increases by 5% every year. Which type of function best models the quantity over time, and why? - Probability of at least one
A fair coin is flipped twice. What is the probability of getting at least one head? - Distance from a fuel rate
A car travels 240 kilometres on 15 litres of fuel. At the same rate, how many kilometres can it travel on 25 litres? - Value outside the plausible range
A random sample of 100 students at a university reported a mean of 7.2 hours of sleep per night, with a margin of error … - Comparing standard deviations by eye
Which of the following data sets has the greatest standard deviation? - Percent increase in a distance
A runner's weekly training distance went from 32 kilometres to 40 kilometres. By what percent did the distance increase? - Comparing unit prices
A 3-kilogram bag of rice costs $7.50, and a 5-kilogram bag of the same rice costs $12.00. Which statement is true? - Strengthening an association into a cause
A survey found that people who take vitamin D supplements report fewer colds than people who don't. Which additional fin… - Spend that predicts a target from a fitted line
A line of best fit relating a shop's monthly advertising spend, x, in thousands of dollars, to its monthly sales, y, in … - What changes the range
The data set 3, 5, 7, 9 has a range of 6. Which of the following changes to the data set would INCREASE the range? - Map scale given as a ratio
A map has a scale of 1 : 50,000, meaning 1 centimetre on the map represents 50,000 centimetres on the ground. Two villag… - Reading a confidence interval correctly
From a random sample of a city's apartments, a researcher reports a 95% confidence interval of 48 to 52 square metres fo… - Recognising a linear decrease
A car's value decreases by $1,500 every year. Which type of function best models the car's value over time, and why? - Tax amount from a total that includes tax
A restaurant bill comes to $108 including an 8% sales tax. How many dollars of the bill is tax? - Flow rate over a longer time
A tap fills a 6-litre bucket in 40 seconds. At this rate, how many litres of water flow from the tap in 2 minutes? - Value plausible under two polls
Two polls of the same population asked the same question. Poll A's result gives a plausible range of 44% to 50% for the … - Prediction from an exponential fit
An exponential curve fitted to a set of data is y = 50(1.2)ˣ. According to this model, what is the predicted value of y … - Probability of a multiple
An integer from 1 to 20 is chosen at random. What is the probability that it is a multiple of 3? - Density as a rate
A block of metal has a mass of 240 grams and a volume of 30 cubic centimetres. What is its density, in grams per cubic c… - Recognising reverse causation
A survey found that people who own more books tend to be in better health. Which of the following alternative explanatio… - Joint probability from a two-way table
If one of the 100 students is selected at random, what is the probability that the student is a tenth grader who is in t… - Mean from percentages of a group
In a class, 40% of the students scored 60 on a test and the remaining 60% scored 85. What is the mean score for the clas… - Currency conversion
One US dollar is worth 0.80 euros. How many euros are 250 US dollars worth? - Wider interval at a higher confidence level
From one random sample, a researcher computed a 90% confidence interval of 40 to 46 grams for a population mean. Which o… - Cost price from a markup
A shop sells a lamp for $70, which is 40% more than the shop paid for it. How many dollars did the shop pay for the lamp… - Time for a shorter distance at the same speed
A car travels 150 kilometres in 2.5 hours at a steady speed. At the same speed, how many MINUTES does it take to travel … - Why a small random sample is useful
A city has about 5 million residents. A survey asks 1,000 residents, selected at random, about their commutes. Which of … - Data that would test a causal claim
A study finds that towns with more public libraries have higher adult literacy rates. Which additional data would most d… - Probability of a double six
Two fair six-sided dice are rolled. What is the probability that the total of the two dice is 12? - Measure most affected by an outlier
A data set of 20 values has one value far larger than all the others. Which of the following measures is most affected b… - Output proportional to the number of machines
Five identical machines make 200 parts in 4 hours. At the same rate, how many parts do 8 of these machines make in 4 hou… - Who a daytime phone survey misses
A survey is conducted by calling home landline numbers between 1 p.m. and 3 p.m. on weekdays. Which group is most likely… - At least one girl among two children
A family has two children, each of whom is equally likely to be a boy or a girl, independently. What is the probability … - Combined percent from two groups
In a school, 30 of the 120 boys and 45 of the 130 girls walk to school. What percent of all the students walk to school? - Plausible values inside an interval
A survey of a random sample of a town's households estimates that the mean number of hours of television watched per wee… - Which conclusion the sample supports
A random sample of 400 registered voters in a city was asked whether they support a new bicycle lane, and 58% said they … - Predicted increase over an interval
A line of best fit for a set of data relating a car's speed x, in kilometres per hour, to its stopping distance y, in me… - Conditional probability from a two-way table
The table shows how 100 students travel to school, by year group. If a student who cycles is chosen at random, what is t… - Original from a percentage of it
In a class, 75% of the students passed a test, and 45 students passed. How many students are in the class? - Interpreting the y-intercept of a model
The number of visitors y to a small museum on a day when x tour buses arrive is modelled by y = 4x + 12. Which of the fo… - Distance on a map from a scale
A map's scale states that 15 centimetres on the map represent 20 kilometres. Two villages are 12 centimetres apart on th… - Identifying the population a sample represents
A researcher surveys a random sample of 300 adults who attend a weekly farmers' market in a city and finds that 82% cook… - Interpreting the slope of a decreasing model
The amount of water y, in litres, in a garden tank t days after a rainstorm is modelled by y = 250 − 12t. Which of the f… - Median of an even-sized data set
The numbers of pets owned by eight families are 8, 3, 5, 2, 8, 4, 7, and 3. What is the median number of pets? - Estimating a population count from a sample proportion
A wildlife officer catches a random sample of 60 fish from a pond and finds that 18 of them are carp. If the pond holds … - Interpreting both parameters of a model
The number of members of a book club t months after it was founded is modelled by n(t) = 20 + 6t. Which statement correc… - Percent increase
A shop's monthly sales rose from $30,000 in April to $40,000 in May. By what percent did sales increase? Round to the ne… - What the margin of error applies to
A poll of 1,000 randomly selected voters finds that 46% intend to vote for Candidate X, with a margin of error of 3 perc… - Interpreting the slope of a line of best fit
A scatterplot shows the relationship between the number of kilometres x a car is driven in a week and the weekly fuel co… - Which measure best represents a typical value
Six houses on a street sold for $50,000, $55,000, $60,000, $60,000, $75,000, and $300,000. Which statement is true? - Percent of a percent
In a school, 60% of the students play a sport, and 50% of the students who play a sport play football. What percent of a… - What happens to the margin of error when the sample shrinks
A poll of 1,600 randomly chosen voters has a margin of error of 2.5 percentage points. If a similar poll were taken with… - What a correlation in observational data supports
A study of 5,000 adults finds that those who eat breakfast daily have lower rates of heart disease. Which conclusion is … - Sample size and confidence
Two surveys estimate the proportion of a city's residents who cycle to work. Survey 1 asked 100 random residents and fou… - Interpreting the slope and intercept of a fitted line
A line of best fit for a scatterplot of a taxi's fare y, in dollars, against distance x, in kilometres, is y = 2x + 15. … - Effect of sample size on margin of error
A survey of 200 randomly chosen residents estimates the proportion who use the park weekly, with a margin of error of 7 … - Choosing a representative sample
A council wants to estimate the proportion of all residents who would use a new evening bus. Which sampling method is mo… - What an observational finding supports
A study of 4,000 adults finds that those who drink tea daily report better sleep than those who do not. Which conclusion… - Generalising from a sample
A survey of 300 randomly chosen members of a city's running club finds that 70% run before 7 a.m. To which group can thi… - Interpreting the intercept and slope of a line of best fit
A line of best fit relating the number of hours t a lamp has been on to the fuel y, in millilitres, left in its reservoi… - Converting a speed to metres per minute
A cyclist rides at an average speed of 24 kilometres per hour. What is this speed in metres per minute? - Original amount before a percent increase
After a 15% raise, an employee's salary is $41,400. What was the salary before the raise, in dollars? - Missing value from a known mean
The mean of five test scores is 80. Four of the scores are 72, 85, 78, and 90. What is the fifth score? - Residual from a line of best fit
A line of best fit for a scatterplot is y = 2.5x + 10. One data point has x = 8 and y = 27. What is the residual (actual… - Probability of neither of two overlapping events
In a class of 40 students, 25 play a sport, 18 play a musical instrument, and 8 do both. If a student is chosen at rando… - Interpreting a margin of error
A random sample of 400 residents of a city was surveyed, and 52% said they support a new park. The margin of error for t… - Why a survey's sample cannot be generalised
A gym wants to know whether all its members would use longer opening hours in the early morning. It surveys the members … - Two spins both red
A spinner has three equal sections coloured red, blue, and green. It is spun twice. What is the probability that both sp… - Scaling a sample proportion to a population
In a random sample of 200 voters from a town of 5,000 voters, 110 said they support a new park. Based on the sample, abo… - Difference between two predictions from a fitted line
A line of best fit relating the hours of sunshine x on a day to the number of ice creams y a stall sells has the equatio… - Final price after a markup and a matching discount
A $60 item is marked up by 15% and then sold at a 15% discount off the marked-up price. What is the final price, in doll… - Probability of a heart or a king
One card is drawn at random from a standard deck of 52 cards. What is the probability that it is a heart or a king? - Estimating a population by capture and recapture
Researchers tagged 300 fish in a lake and released them. Later they caught a random sample of 80 fish, of which 12 were … - Cement in a concrete mix
Concrete mix is made from cement and sand in the ratio 1 : 4 by mass. A builder needs 60 kilograms of the mix. How many … - Length of a scale model
A model railway is built at a scale of 1 : 87. A real railway carriage is 26.1 metres long. How long is the model of the… - Meal total with tax and tip
A meal costs $45 before tax. Sales tax of 6% is added to the $45, and the customer also leaves a tip equal to 20% of the… - Median after increasing the largest values
A data set of 7 values has a median of 14. The two largest values are each increased by 10, and no other value changes. … - Height gain from a linear model
The model h = 2.4a + 50 gives the height h, in centimetres, of a certain kind of shrub at age a years. According to the … - Probability of liking neither drink
Of 200 people surveyed, 120 said they like tea, 90 said they like coffee, and 40 said they like both. If one of the 200 … - Cycling speed in metres per minute
A cyclist rides at a steady 18 kilometres per hour. How many metres does the cyclist travel each minute? - Seats before a reduction
After 12% of the seats in a theatre were removed, the theatre had 440 seats. How many seats did it have before the remov… - Median from the two middle values
A data set has 10 values. When the values are listed in order, the 5th value is 14 and the 6th value is 18. What is the … - Plausible population value from a poll
In a random sample of 200 voters, 56% said they favour a new library. The margin of error for the estimate is 4 percenta… - Real length from a house plan
A plan of a house is drawn at a scale of 1 : 50. A wall that is 8 centimetres long on the plan is how many metres long i… - Membership before a year's growth
The membership of a club grew by 5% over a year to 8,400. What was the membership a year earlier? - Mean after doubling every value
A data set of 8 values has a mean of 6. Every value in the set is then doubled. What is the mean of the new data set? - y-intercept of a line through data points
The points (2, 3), (4, 7), (6, 11), and (8, 15) all lie on a single line in the xy-plane. What is the y-coordinate of th… - Two blue draws with replacement
A bag contains 5 red marbles and 3 blue marbles. One marble is drawn at random and put back, and then a second marble is… - Flaw in a comparison of teaching methods
A school tested two teaching methods by using method A with its strongest mathematics students and method B with the res… - Scaling a mixture
A paint mixture uses 3 parts blue to 4 parts white. How many millilitres of blue are needed to go with 200 millilitres o… - Rent after a percent rise
A monthly rent of $250 is increased by 12%. What is the new monthly rent, in dollars? - Mode of a data set
A data set is 5, 5, 6, 8, 9, 9, 9, 12. What is the mode? - Probability of two aces from a small deck
A deck of 20 cards contains 4 aces. Two cards are drawn at random without replacement. What is the probability that both… - Spotting a misleading comparison
A shop advertises that its sales 'rose by 200 percent' after a redesign. Its records show sales of 3 items in the week b… - Flour for a larger batch of rolls
A recipe uses 250 grams of flour to make 4 bread rolls. At the same rate, how many grams of flour are needed to make 40 … - Percent increase in attendance
Attendance at a weekly market rose from 60 stalls to 66 stalls. By what percent did the number of stalls increase? - New mean after adding a value
Four numbers have a mean of 20. A fifth number, 30, is added to the set. What is the mean of the five numbers? - Prediction from a line of best fit
For a set of data, the line of best fit is y = 20x + 15. What y-value does the line predict when x = 4? - Two defective bulbs in a row
A box holds 10 light bulbs, 3 of which are faulty. Two bulbs are taken out at random without replacement. What is the pr… - Conclusion from a randomised fertiliser experiment
Researchers randomly assigned 200 tomato plants to two groups. One group received a new fertiliser and the other did not… - Fuel for a longer journey
A car travels 150 kilometres on 10 litres of fuel. At the same rate, how many litres of fuel does it need to travel 375 … - Price before a discount
After a 15 percent discount, a coat costs 68 dollars. What was the price of the coat, in dollars, before the discount? - Change predicted by a linear model
A model for a company's sales y, in thousands of dollars, against its advertising spending x, in thousands of dollars, i… - Price after a percent rise and a fixed cut
A shop raises the price of a 60-dollar item by 15 percent and then reduces the new price by 10 dollars. What is the fina… - Mean after adding a constant to every value
A data set of 8 numbers has a mean of 15. If 3 is added to each of the 8 numbers, what is the mean of the new data set? - Probability of studying exactly one language
Of 60 students, 35 study French, 20 study Spanish, and 5 study both. If a student is chosen at random, what is the proba… - Design to test whether breakfast raises scores
Researchers observed that students who eat breakfast tend to score higher on morning tests. Which study design would bes… - Probability after one sweet is removed
A jar holds 20 sweets: 8 red, 7 green, and 5 yellow. One red sweet is taken out and eaten. If one of the remaining sweet… - Alternative explanation for an association
A study finds that people who drink more coffee sleep fewer hours. Which of the following is an alternative explanation …
Hard (133)
- Statistics: mean
The mean of five numbers is 12. If four of them are 8, 10, 14, and 16, what is the fifth number? - Overlapping sets
In a survey of 50 people, 30 like coffee, 20 like tea, and 8 like both. How many like neither? - Average speed
A car travels at 60 mph for 2 hours, then 40 mph for 3 hours. What is its average speed for the whole trip? - Standard deviation concept
Which statement correctly compares the standard deviations of the two sets? - Line of best fit interpretation
Which statement best interprets the slope of the line of best fit? - Percent concentration / mixture (weighted percent) problems
How many milliliters of the 40% acid solution must the chemist add? - Reverse percent with weighted parts of a whole
How many circuit boards were produced in the batch? - Recovering the margin of error from an interval
What is the margin of error for this estimate, in grams? - Studies with neither random selection nor random assignment
Which conclusion is best supported by this study? - Slope of a line of best fit from two points
What is the slope of this line of best fit? - Proportion from a recipe
A recipe uses 2 cups of flour for every 3 eggs. How many cups of flour are needed for 12 eggs? - Percent change
A store's monthly sales rose from $40,000 to $50,000. By what percent did sales increase? - Combined mean of two groups
In one class of 10 students the mean test score was 80. In another class of 20 students the mean was 86. What is the mea… - Converting a speed between unit systems
A cyclist travels at 72 kilometres per hour. What is this speed in metres per second? (1 kilometre = 1,000 metres; 1 hou… - Successive percent changes
A stock's price rises by 20% one month and then falls by 20% the next month. Compared with its price at the start, the p… - Comparing standard deviations
Data set A consists of the values 10, 10, 10, 10. Data set B consists of the values 1, 10, 10, 19. Which statement is tr… - Conditional probability from counts
Of the 50 plants in a study, 30 were watered daily and 20 were watered weekly. Of the daily-watered plants, 24 bloomed. … - What a randomised experiment supports
A hospital selected 200 of its patients at random and randomly assigned each of them to one of two post-surgery diets. P… - Identifying a confounding variable
A study found that towns with more ice-cream shops per resident have higher rates of sunburn. A journalist concludes tha… - Probability of neither of two events
At a school, 40% of the students take chemistry, 30% take physics, and 15% take both. If a student is selected at random… - Effect of removing an outlier
The data set 3, 7, 8, 12, 40 has one unusually large value, 40. If 40 is removed from the data set, which of the followi… - Sharing in a ratio
A prize of $840 is shared among three people in the ratio 2 : 3 : 7. How many dollars does the person with the largest s… - Extrapolating along a line of best fit
The line of best fit for a scatterplot passes through the points (0, 8) and (10, 28). According to this line, what is th… - Scaling every value in a data set
Every value in a data set is multiplied by 3 to form a new data set. Which of the following statements about the new dat… - Combining two percent increases
A town's population increased by 10% in one year and then by 20% in the following year. By what percent did the populati… - Confidence level and interval width
From one random sample, a researcher computes two intervals for a population mean: one at a 90% confidence level and one… - Capacity from a change in percent full
A water tank is 40% full. After 150 litres are added, it is 70% full. What is the capacity of the tank, in litres? - Line matching a falling scatterplot
A scatterplot shows the points (1, 10), (2, 8), (3, 6) and (4, 4). Which equation best represents the line of best fit f… - Design feature that permits a causal conclusion
A study found that schools which adopted uniforms saw improved attendance the following year. Each school had decided fo… - Extending a doubling pattern
According to the table, y doubles each time x increases by 3. What is the value of y when x = 9? - Conditional probability from a two-way table
If a person who owns a bicycle is chosen at random from those surveyed, what is the probability that the person is under… - Why two random samples differ
Two researchers each select a random sample of 300 households from the same city and compute the mean household size. On… - Two draws with replacement
A jar contains 5 red marbles and 3 green marbles. A marble is drawn at random, replaced, and a second marble is drawn at… - Scaling a sample mean to a population total
A random sample of 40 students at a school with 1,200 students reported a mean of 3.1 hours of homework per week. Based … - At least one success in two independent tries
Each time a player takes a free throw, the probability of scoring is 0.2, independently of other throws. What is the pro… - Median unchanged by balanced extremes
The data set 4, 6, 8, 10, 12 has a median of 8. The values 1 and 20 are added to the data set. What is the median of the… - Why participants are not told their group
In a trial of a new headache tablet, half the participants receive the tablet and half receive a placebo that looks iden… - Same mean, different spread
Data set P consists of the values 10, 20, 30, 40. Data set Q consists of the values 22, 24, 26, 28. Which statement is t… - Sample size for a target margin
A pilot poll of 400 randomly selected people produced a margin of error of 4 percentage points. The margin of error shri… - Point farthest from the line of best fit
The table shows the actual y-value and the y-value predicted by a line of best fit at four values of x. At which value o… - Percent of a percent in two steps
A company with 250 employees laid off 20% of them. It later rehired 10% of the employees it had laid off. How many emplo… - Why attendance and weight loss may not be cause and effect
A gym reports that members who attend at least three times a week lose more weight than members who attend less often, a… - Table showing a constant percent decrease
A quantity decreases by the same PERCENT each year. Which of the following tables of yearly values could show this quant… - Neither of two independent events
On each of two days, the probability of rain is 0.3, independently of the other day. What is the probability that it doe… - Set whose mean exceeds its median
For which of the following data sets is the mean GREATER than the median? - Growth factor from a table
The table shows the value of y for three consecutive values of x. Each time x increases by 1, y is multiplied by the sam… - Two draws without replacement
A bag contains 3 red marbles and 2 blue marbles. Two marbles are drawn at random, one after the other, WITHOUT replaceme… - Map distance from a scale
On a map, 3 centimetres represent 45 kilometres. Two towns are 150 kilometres apart. How far apart, in centimetres, are … - What barely affects a margin of error
Which of the following has the LEAST effect on the margin of error of a well-conducted random sample survey? - How far a data point sits above a model
A model predicts the height h of a seedling, in centimetres, from its age d in days: h = 20 + 0.8d. A seedling that is 5… - Median above the mean
The data set 1, 9, 10, 12 has a mean of 8. Which statement about the median of the data set is true? - Bill with tax and a tip
A restaurant meal costs $80 before tax. A 5% sales tax is added, and the customer leaves a tip equal to 15% of the pre-t… - Turns of a driven gear
A gear with 12 teeth turns 5 full times, driving a second gear with 20 teeth. How many full turns does the second gear m… - Effect of a larger sample on the interval
A researcher estimates the mean weight of apples in an orchard from a random sample of 50 apples and reports a margin of… - Recognising a decreasing but flattening trend
The table shows the number of a certain rare bird counted in a reserve in each of five years. Which of the following bes… - Fifth value from a known mean
Five friends recorded how many books each read last year. Four of them read 12, 15, 15, and 18 books. If the mean for al… - Two successive discounts
A coat priced at $200 is marked down by 20%. A week later, the marked-down price is reduced by a further 15%. What is th… - Converting km/h to m/s
A train travels at 90 kilometres per hour. What is its speed in metres per second? - What a correlation does and doesn't show
A study of 800 adults found that those who ate breakfast regularly had, on average, lower body weight than those who ski… - Probability of two dependent draws
A drawer holds 5 socks: 2 black and 3 white. Two socks are taken out at random one after the other without replacement. … - Comparing spread with equal means
Two data sets have the same mean. Set P: 10, 11, 12, 13, 14. Set Q: 2, 8, 12, 16, 22. Which of the following is true? - Raising and lowering by the same percentage
A share price rises by 25% one week and falls by 25% the next. Compared with its starting price, the share price at the … - Which sample gives the most reliable estimate
A researcher wants to estimate the mean commute time of all employees at a large company. Four sampling plans are propos… - Predicting from a line through data
The table shows the number of pages y a student had read x minutes after starting a book. The data lie exactly on a line… - Percent increase versus percent decrease between the same two numbers
A town's population grew from 12,000 to 15,000 over a decade. Which of the following statements is true? - Recognising a confounding explanation
A study finds that towns with more ice-cream shops have higher rates of sunburn. Which of the following is the most reas… - Describing an association from a scatterplot summary
In a scatterplot, each point shows a car's age x, in years, and its resale value y, as a percentage of its original pric… - Probability from a two-way table (marginal)
The table shows 120 pets at a shelter by type and age group. If one pet is chosen at random, what is the probability tha… - Price before a markup
A store marks up the wholesale cost of a jacket by 15% to get its selling price of $276. What was the wholesale cost, in… - Total from a ratio and a difference
In a choir, the ratio of altos to sopranos is 3 to 5. There are 6 more sopranos than altos. How many singers are in the … - Recognising the limits of a before-and-after comparison
A gym reports that members who joined its new fitness programme lost an average of 4 kilograms over three months. Which … - Mean after adding a value
The mean of five test scores is 80. A sixth test is taken, and the mean of all six scores becomes 82. What was the score… - Map distance from a ratio scale
A map has a scale of 1 : 50,000, meaning 1 centimetre on the map represents 50,000 centimetres on the ground. Two villag… - Reading a sample statistic versus a population parameter
A biologist measures the wingspans of 50 randomly caught birds of a species and finds a mean of 24.1 cm with a margin of… - Comparing two estimates with margins of error
Two random samples estimate the proportion of defective parts from two machines. Machine A: 4% ± 1%. Machine B: 6% ± 3%.… - Recognising a selection bias
A hotel emails a satisfaction survey to guests who booked directly through its website, and 92% of respondents rate thei… - Choosing the model that fits a table
The table shows the water level y, in metres, in a reservoir x weeks into a drought. Which equation models the relations… - Probability that at least one of two spins is not red
A spinner lands on red with probability 1/4 on each spin, and spins are independent. If it is spun twice, what is the pr… - Interpreting a margin of error
A random sample of 500 households finds that 36% own a bicycle, with a margin of error of 4 percentage points. Which of … - Identifying a confounding factor
A study finds that towns with more coffee shops have higher average incomes. Which of the following is the most reasonab… - Predicting from a line through data
The table shows the number of pages y a copier had printed x minutes after being switched on. The data lie exactly on a … - Probability of a union with overlap on a spinner
A spinner has 8 equal sectors numbered 1 through 8, and it is spun once. What is the probability that the spinner lands … - Combined effect of two successive discounts
A coat is reduced by 30%, and the sale price is then reduced by a further 10%. What is the total percent reduction from … - Effect of an outlier on the mean
The data set 8, 10, 10, 12 has an additional value of 30 added to it. By how much does the mean increase? - Probability of two draws without replacement
A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn at random without replacement. What is the probab… - Map scale with a non-unit ratio
On a map, 2 centimetres represent 5 kilometres. A footpath measures 7.5 centimetres on the map. How many kilometres long… - Fuel for a longer trip
A car uses 6 litres of fuel for every 100 kilometres. How many litres will it use on a 250-kilometre trip? - Enlarging a photo in proportion
A photograph measures 4 inches by 6 inches. It is enlarged so that its shorter side becomes 10 inches, keeping the same … - Which sample mean to trust more
Two random samples of households were taken from the same town to estimate the town's mean weekly grocery spending. Samp… - Coffee and insomnia
A study finds that adults who drink coffee every day report insomnia more often than adults who do not. Which of the fol… - Converting a running speed to kilometres per hour
A runner covers 400 metres in 80 seconds. What is the runner's average speed in kilometres per hour? - Effect of sample size on a margin of error
Two random polls estimate support for the same candidate. Poll A surveys 400 voters and Poll B surveys 1,600 voters. Pol… - Comparison undermined by who gets the treatment
A hospital reports that patients given a new drug recover faster than patients who are not given it. The drug is prescri… - Snail speed converted to metres per hour
A snail moves at a steady 4 millimetres per second. How many metres does it move in one hour? - Litres from a flow rate in millilitres
Water flows from a tap at 250 millilitres per second. How many litres flow in 4 minutes? - Net percent change after a rise and a fall
A price is increased by 25% and the new price is then decreased by 40%. The final price is what percent less than the or… - Percent of a percent of a class
Of the 400 students in a school, 30% take art. Of the students who take art, 25% also take music. How many students take… - Effect of removing an outlier on the mean
The data set 6, 8, 10, 12, 44 has one outlier, 44. If the outlier is removed, by how much does the mean of the data set … - Residual of a data point
For a set of data, the line of best fit is y = 0.8x + 12. One of the data points is (20, 31). What is the residual for t… - Conditional probability among instrument players
In a class of 60 students, 25 play a musical instrument, and 15 of those 25 also sing in the choir. If a student who pla… - Effect of sample size on the margin of error
Two polls of the same population are run with the same method and find the same result. Poll A surveys 400 people and Po… - Paint for two coats on a wall
A wall is 6 metres wide and 2.5 metres high. One litre of paint covers 12 square metres. How many litres are needed to g… - Train speed from its length and passing time
A train 200 metres long passes a signal post completely in 8 seconds. What is the speed of the train, in kilometres per … - Bill before a service charge
A restaurant bill of $84 includes a 12% service charge added to the cost of the food. What was the cost of the food, in … - Combined mean of two classes
Class A has 20 students with a mean test score of 70. Class B has 30 students with a mean test score of 80. What is the … - Extending an exact exponential fit
The data points (1, 5), (2, 10), (3, 20), and (4, 40) fit an exponential model exactly, with y doubling each time x incr… - Probability from two overlapping groups
In a class of 50 students, 30 play football. Of those 30, 20 also swim. Of the 20 students who do not play football, 10 … - Margin of error from an interval
A poll reports that the percent of voters who support a proposal is 48% to 54%, an interval formed by adding and subtrac… - Flaw in concluding cause from an observation
A school finds that students who eat breakfast score higher on tests than students who do not. The school concludes that… - Judging a claim of cause from a comparison
A study finds that towns with more bicycle lanes have lower rates of heart disease. A council concludes that building bi… - Litres lost from a dripping tap in a day
A tap drips 4 millilitres of water every 10 seconds. How many litres does it drip in one day? - Percent increase in a bill
A household's monthly water bill rose from $60 to $66. By what percent did the bill increase? - Change in median when a large value is added
A data set is 3, 5, 8, 12, 20. A sixth value, 100, is added. By how much does the median increase? - Residual from a line of best fit
The line of best fit for a data set is y = 2x + 10. One data point is (15, 42). What is the residual for this point, the… - Probability that two draws are not both red
A box holds 3 red and 2 blue pens. Two pens are taken out at random without replacement. What is the probability that th… - Effect of a larger sample on an estimate
Two random samples are drawn from the same city to estimate the share of residents who cycle to work. Sample A has 200 p… - Judging a claim of cause from an observation
A study finds that students who bring a water bottle to exams score higher on average than those who do not. A school co… - Distance from a speed in metres per second
A runner moves at a steady 2 metres per second. How many kilometres does the runner cover in one hour? - Original price from a sale price
After a 25% discount, a jacket costs $45. What was its price, in dollars, before the discount? - Mean of a combined group
Six children have a mean age of 10, and four adults have a mean age of 15. What is the mean age of all ten people? - Difference in predictions from a line of best fit
For a set of data, the line of best fit is y = 4x + 7. By how much does the predicted y-value at x = 8 exceed the predic… - Probability that two cards are not both hearts
A pack of 8 cards contains 3 hearts. Two cards are drawn at random without replacement. What is the probability that the… - Interpreting a margin of error
A random sample of city residents gives an estimate that 62% support a new park, with a margin of error of 3 percentage … - Judging a conclusion from a comparison of two groups
A hospital finds that patients who receive visitors recover faster than patients who do not. It concludes that arranging… - Seventh value that raises a mean
A data set of 6 values has a mean of 20. When a seventh value is added, the mean of the 7 values is 22. What is the seve… - Probability of playing neither
Of 80 students, 50 play a sport, 30 play an instrument, and 15 do both. If a student is chosen at random, what is the pr… - Conclusion from an observed association
Researchers observed that people who own more books tend to score higher on a vocabulary test. Which of the following co… - Original value before two percent changes
A number is increased by 20 percent, and the result is then decreased by 25 percent, giving 90. What was the original nu… - Choosing a model from a table
A table gives pairs (x, y): (1, 3), (2, 6), (3, 12), (4, 24). Which of the following models fits these data? - Number of red pens from a probability
A box contains only red pens and blue pens. The probability of drawing a red pen at random is 2/5. If there are 12 blue … - Sample size needed to halve a margin of error
A survey of 400 randomly chosen people has a certain margin of error. About how many people should a new survey include … - Limits of a randomised trial's result
In a randomised trial, adults who took a supplement slept 20 minutes longer on average than adults given a placebo. A he… - Two sample means from one population
Two random samples of 100 people are drawn from the same city. The first has a mean age of 52 years and the second a mea…
Very hard (135)
- Compound percent / successive discounts
An item priced at $200 is first marked down by 20%, and then an additional 10% is taken off the reduced price. What is t… - Probability with mean constraint
A data set of 6 test scores has a mean of 78. After a 7th score is added, the mean rises to 80. What was the 7th score? - Conditional probability from category counts (reversing the condition)
If one of the chips that failed inspection is selected at random, what is the probability that it was produced by Machin… - Reversing a chain of percent changes
The regular price of a bicycle at a shop was increased by 25%. Later, during a sale, this increased price was reduced by… - Median and mean from a frequency table with unknown frequencies
What is the result when the mean number of pets is subtracted from the median number of pets? - Repeated proportional dilution (percent concentration)
What is the value of x? - The population a sample estimate describes
Which conclusion is best supported by these results? - Random selection and random assignment together
Which conclusion is best supported? - Limits of predictions from a model
Which of the following is the best criticism of this prediction? - Expected number from a probability
A factory finds that the probability a randomly selected part is defective is 0.15. If 400 parts are selected at random,… - Mean from a frequency distribution
On a test, 3 students scored 70, 5 students scored 80 and 2 students scored 100. What is the mean score of the 10 studen… - Generalising to the right population
A researcher wants to estimate the mean daily commute time of adults in a certain state. She surveys 600 adults selected… - Reading a negative slope without overclaiming
For 30 cars, a scatterplot shows each car's mass, x, in kilograms, and its fuel economy, y, in kilometres per litre. The… - Original price from a discount then tax
A jacket is sold at a 15% discount, and then 8% sales tax is added to the discounted price. The customer pays $91.80. Wh… - Combining two ratios
The ratio of a to b is 3 : 4, and the ratio of b to c is 6 : 5. What is the ratio of a to c? - Two flaws in a causal claim
A magazine posted a survey online for its readers. Among readers who responded, those who said they drank green tea ever… - Probability of independent events all occurring
In a certain game, the probability that a player wins any single round is 0.2, and rounds are independent of one another… - Reconciling two polls
Two polls of the same population asked the same question. Poll 1 surveyed 400 randomly selected people: 52% in favour, m… - Value removed from a data set
The mean of 8 test scores is 70. When the lowest score is removed, the mean of the remaining 7 scores is 74. What was th… - Sample size needed to halve a margin of error
A researcher's random sample gives an estimate with a certain margin of error. Keeping the confidence level the same, th… - Reversing one discount to apply another
After a 20% discount, a lamp costs $96. What would the lamp cost, in dollars, with a 10% discount off the original price… - Overstating certainty from a poll
A poll of 1,000 randomly selected adults found that 62% oppose a policy, with a margin of error of 3 percentage points. … - Group size from a combined mean
A class of 24 students has a mean test score of 70. A second class has a mean score of 82. When the two classes are comb… - Average speed for a round trip
A cyclist rides 60 kilometres from home to a lake at an average speed of 30 kilometres per hour, then rides straight bac… - Conclusion that a volunteer trial cannot support
Two hundred adults who volunteered for a study were randomly assigned either to a new exercise programme or to their usu… - Percent increase that reverses a decrease
A price is reduced by 20%. By what percent must the reduced price be increased to return to the original price? - Margin of error at a larger sample size
For a random sample of 100 people, a poll's margin of error is 6 percentage points. The margin of error shrinks in propo… - Count from a probability with an unknown
A bag contains r red marbles and 8 blue marbles. If the probability of drawing a red marble at random is 1/3, what is th… - Original price from two successive discounts
A coat's price was reduced by 10%, and the reduced price was then reduced by a further 15%. The final price is $153. Wha… - Strongest evidence for a causal link
Surveys consistently find that students who sleep more score higher on exams. Which of the following would provide the S… - Change that leaves the median alone
The data set 5, 8, 9, 12, 15 has a median of 9. Which of the following changes to the data set would NOT change the medi… - Sample size for a third of the margin
A random sample of 200 people gives an estimate with a certain margin of error. The margin of error shrinks in proportio… - Percent change versus percentage points
In one year, support for a proposal rose from 20% of voters to 25% of voters. By what PERCENT did the level of support i… - Flaw in comparing completers with dropouts
In a trial of a new medicine, patients who completed the full course recovered faster on average than patients who dropp… - A rise and a discount that cancel
A shop raised the price of a coat by 25% and later offered 20% off the new price. The final price is what percent of the… - Interpreting a placebo effect
In a trial, patients who were given a sugar pill and told it was a painkiller reported less pain than patients who were … - Exactly two heads in three flips
A fair coin is flipped three times. What is the probability of getting exactly two heads? - Why an experiment beats an observational study here
A study finds that adults who drink green tea daily have lower blood pressure, on average, than adults who do not. A res… - Comparing two intervals that overlap
Two random samples of the same size were taken from two lakes. The mean length of fish in Lake A was estimated as 24 cm … - Choosing between linear and exponential from ratios
The table shows the height y, in centimetres, to which a ball rises after x bounces. Which equation best models the rela… - Combined rate of two machines
Machine A can fill 180 bottles in 45 minutes, and Machine B can fill 120 bottles in 40 minutes. Working together at thes… - Why a difference might not be meaningful
In a random sample of 40 students at a school, the mean height of the 20 left-handed students was 1 cm greater than that… - Probability from a two-way table with a complement
The table shows the results of a survey of 200 commuters about their travel mode and whether they arrived late at least … - Effect on the median of changing an extreme value
A data set of 11 values has a median of 30. The largest value in the set is 90. If the largest value is changed to 150 a… - Converting metres per second to kilometres per hour
A cyclist rides at 2 metres per second. What is the cyclist's speed in kilometres per hour? - Interpreting a confidence interval correctly
A random sample of a city's households gives a 95% confidence interval of 2.4 to 2.8 for the mean number of people per h… - Comparing mean and median in a skewed set
The salaries at a small company are $40,000 for each of nine employees and $400,000 for the owner. Which statement is tr… - Comparing margins of error from different sample sizes
Two random samples are drawn from the same large population to estimate the same proportion. Sample 1 has 100 people and… - Interpreting a residual
A line of best fit predicts that a house with 3 bedrooms sells for $310,000. One particular 3-bedroom house sold for $29… - Probability of at least one success
A basketball player makes a free throw with probability 1/4, and each throw is independent. If the player takes two free… - Reverse percentage change
After a 40% discount, a coat costs $90. Which of the following is closest to the percent increase needed to bring the di… - Choosing the sample that best supports generalisation
A researcher wants to estimate the average time all students at a university spend commuting. Which sample would best su… - Designing a fair comparison
A farmer wants to test whether a new fertiliser increases wheat yield. Which design gives the most reliable comparison? - Extrapolation caution
A line of best fit relating a child's age x (from 2 to 10 years) to height y in centimetres is y = 6x + 78. Which statem… - Comparing precision of two estimates
Two random samples estimate the mean height of trees in two woods. Wood P: mean 14.0 m, margin of error 0.5 m, from 400 … - Strengthening a causal claim
A gardener reports that tomato plants she fed with a new fertiliser produced more fruit than plants she fed with the old… - Choosing between models from a scatterplot description
A scatterplot shows a town's population every ten years from 1900 to 2000. The points rise slowly at first and then more… - Filling time with a unit conversion
A tap delivers 3.5 litres of water per minute. How many minutes does it take to fill a tank with a capacity of 0.42 cubi… - Ratio of a combined mixture
Mixture A is sand and cement in the ratio 3 : 2 by mass. Mixture B is sand and cement in the ratio 1 : 1. If 10 kilogram… - Time for a train to clear a platform
A train 200 metres long passes a signal post completely in 8 seconds. Travelling at the same speed, how many seconds doe… - Area on a map to real area
On a map with a scale of 1 : 50,000, a lake covers an area of 4 square centimetres. What is the real area of the lake, i… - Inverse proportion between workers and time
Six workers, all working at the same rate, build a wall in 10 days. How many days would 4 such workers take to build the… - Residual from a line of best fit
A scatterplot shows the number of hours x that students studied and their test scores y. The line of best fit is y = 1.8… - Extending an exponential pattern
The table shows the number of infected plants y in a greenhouse t weeks after a fungus was first found. t | y 0 | 3 1 |… - Interpreting the slope of a fitted line
A rental company fits the line c = 0.4m + 15 to data on the cost c, in dollars, of one-day van rentals driven m miles. W… - Choosing an inverse model
The table shows the time y, in hours, that a job takes when x workers share it equally. x | y 1 | 10 2 | 5 4 | 2.5 Whi… - Conditional probability from a two-way table
The table summarises 120 adults by whether they own a bicycle and whether they own a car. | Owns a car | No car | Total… - Two committee members both from one group
A school council has 4 teachers and 6 parents. Two members are selected at random to form a committee, and no member can… - Complement of all failing
A building has three independent smoke alarms, and each has a probability of 1/5 of failing during a fire. What is the p… - Mean after removing a value
The mean of a list of 5 numbers is 20. When the number 32 is removed from the list, what is the mean of the remaining 4 … - Effect of an outlier on mean and median
The data set 2, 3, 3, 4, 5, 6, 40 gives the number of minutes seven customers waited. Which statement about the mean and… - Converting a speed across two units
A train travels at 54 kilometres per hour. What is its speed in metres per second? (1 kilometre = 1,000 metres) - What a margin of error does and does not say
A random sample of 400 households in a city found that 36% recycle weekly, with a margin of error of 5 percentage points… - Confounding in a comparison of two groups
Pupils who chose to attend an optional after-school maths club scored higher on average on the end-of-year exam than pup… - Distance from a ratio scale
A map has a scale of 1 : 25,000. Two farms are 6.4 centimetres apart on the map. How many kilometres apart are the farms… - Density of a metal block
A rectangular block of metal measures 2 cm by 3 cm by 5 cm and has a mass of 240 grams. What is the density of the metal… - Percent decrease that undoes a percent increase
A price is increased by 25%. By what percent must the new price be decreased to return it to the original price? - Percent of a percent of a total
In a survey of 1,200 people, 45% were under 30 years old, and 40% of those under 30 said they own a bicycle. How many of… - Value that raises a mean
A list of 7 numbers has a mean of 12. When an eighth number is added to the list, the mean of the 8 numbers is 13. What … - Comparing spread with equal centres
Data set A is 10, 12, 14, 16, 18. Data set B is 2, 12, 14, 16, 26. Which of the following statements is true? - Change in a prediction from a slope
The line of best fit for a scatterplot has the equation y = −2.5x + 90. When x increases by 4, by how much does the pred… - Choosing an exponential model from a table
The table shows the amount y of a medicine, in milligrams, in a patient's blood x hours after a dose. x | y 0 | 100 1 |… - Probability of belonging to neither group
Of 200 students, 120 play a sport, 80 play in the band, and 50 do both. If one student is chosen at random, what is the … - Probability of a particular sum on two spins
A spinner has 8 equal sections numbered 1 to 8. It is spun twice. What is the probability that the two numbers add up to… - What reduces a margin of error
A poll of 1,000 randomly selected voters reports a margin of error of 3 percentage points. Which of the following change… - Fuel cost of a trip
A car travels 40 miles on each gallon of fuel, and fuel costs $4 per gallon. How many dollars does the fuel for a 300-mi… - Net change after a fall and a rise
A town's population fell by 20% between 2010 and 2020 and then rose by 25% between 2020 and 2030. By what percent did th… - Effect on mean and median of raising the largest value
A data set has five values with a mean of 20 and a median of 18. The largest value is increased by 10 and the other valu… - Point with a positive residual
A line of best fit has slope 0.9 and passes through the point (10, 15). Which of the following data points has a positiv… - At least one six in three rolls
A fair six-sided die is rolled three times. What is the probability that at least one of the rolls shows a six? - Sample size for a smaller margin of error
A survey of 625 randomly chosen residents gives an estimate with a margin of error of 4 percentage points. Approximately… - Edge of a cube from mass and density
A solid cube of aluminium has a mass of 2,700 grams. The density of aluminium is 2.7 grams per cubic centimetre. What is… - Chained percentage comparisons
Population A is 20% larger than population B, and population B is 25% smaller than population C. Population A is what pe… - Mean of the remaining values
The mean of 5 numbers is 12. The mean of 3 of those numbers is 8. What is the mean of the other 2 numbers? - Point above a line of best fit
A scatterplot has the line of best fit y = −2x + 50. One point on the scatterplot has x-coordinate 10 and lies 6 units a… - Total probability across two groups
In a club, 40% of the members are students. Three quarters of the student members and one half of the non-student member… - Turns of a small gear
Two gears mesh so that their teeth move together. The larger gear has 40 teeth and the smaller gear has 15 teeth. When t… - Concentration of a mixed drink
Three litres of a drink that is 10% fruit juice are mixed with 2 litres of a drink that is 25% fruit juice. What percent… - Original price before two discounts
A coat's price was reduced by 20%, and the reduced price was then cut by a further 15%. The final price was $170. What w… - Prediction from a doubling model
The population of a colony of bats is modelled by P(t) = 50 · 2^(t/5), where t is the number of years after the colony w… - Sample size needed to halve a margin of error
A researcher wants to halve the margin of error of a survey estimate while keeping the same method and confidence level.… - Average speed over two legs
A driver covers the first 90 kilometres of a trip at an average speed of 60 kilometres per hour and the next 90 kilometr… - Reverse percentage comparison
Quantity A is 25% greater than quantity B. Quantity B is what percent less than quantity A? - Range after raising the smallest value
A data set of 9 values has a range of 20. The smallest value is increased by 5, and it remains the smallest value. No ot… - Yearly percent decrease in a decay model
The number of cars of a certain model sold each year is modelled by C(t) = 200(0.8)ᵗ, where t is the number of years aft… - Probability that at least one of two independent events occurs
Two independent events have probabilities 0.3 and 0.5. What is the probability that at least one of the two events occur… - Interpreting a confidence interval
From a random sample, researchers estimate that the mean height of adult men in a city is 176 centimetres, with a 95% co… - Evaluating a claim about a treatment from a trial design
A clinic gives a new sleep treatment to 50 patients who asked for it and compares their sleep with 50 patients who did n… - Reading a percentage change correctly
A newspaper reports that a town's crime rate 'doubled' last year. The police figures show 2 burglaries the year before a… - Converting a leak rate to litres per second
A pipe leaks 5 cubic metres of water per hour. To the nearest hundredth, how many litres does it leak per second? (1 cub… - Net effect of a fall and a rise
A share price falls by 20% in one week and then rises by 20% the next week. The final price is what percent of the origi… - Actual value from a residual
The line of best fit for a data set is y = −3x + 60. A point on the scatterplot at x = 6 has a residual of +3, meaning i… - Two taps filling a tank together
One tap can fill a tank in 6 hours and a second tap can fill the same tank in 3 hours. If both taps run together, how ma… - Working back from a marked-up price
A shop adds a 20% markup to what it pays for each item. It sells a lamp for $240. How many dollars did the shop pay for … - Comparing spreads of two data sets
Data set P is 10, 10, 10, 10, 10. Data set Q is 2, 6, 10, 14, 18. Which statement about the two sets is true? - Reading the meaning of a y-intercept in context
A scatterplot of the ages of 40 trees and their trunk widths has the line of best fit w = 0.6a + 5, where w is width in … - Probability that two balls match in colour
A bag holds 2 red balls and 2 blue balls. Two balls are drawn at random without replacement. What is the probability tha… - Largest value from mean, median and mode
A list of five positive integers has a mean of 6, a median of 5, and a single mode of 3, which appears exactly twice. Wh… - Conditional probability from survey counts
In a survey of 200 people, 120 own a car, and 90 of those also own a bicycle. Of the 80 people who do not own a car, 50 … - Interpreting a poll with a margin of error
A poll of 400 randomly selected voters estimates support for a measure at 52 percent, with a margin of error of 5 percen… - Comparing margins of error for two sample sizes
Two random samples are drawn from the same population to estimate its mean. Sample A has 100 people and sample B has 900… - Evaluating a conclusion about libraries and incomes
A study found that towns with more libraries have higher average incomes. A council concludes that building a new librar… - Generalising from a survey outside a bicycle shop
To estimate the proportion of a city's residents who cycle to work, a researcher surveys 1,000 people leaving a bicycle … - Real distance from a map scale
A map has a scale of 1 to 25,000. Two towns are 14 centimetres apart on the map. What is the actual distance between the… - Population after a rise and a fall
A town's population grew by 10 percent in one year and fell by 10 percent the next year. The population at the end of th… - Overall percent from two groups
In a survey, 40 percent of the respondents were men and the rest were women. Of the men, 30 percent said yes to a questi… - Largest possible value given a mean and a median
Five positive integers have a mean of 10 and a median of 12. What is the greatest possible value of the largest of the f… - Limits of a fitted linear model
A researcher fits the model y = 20 − 0.5x to data on x, the daily outdoor temperature in degrees Celsius between 0 and 3… - Conditional probability among those who do not play tennis
In a class of 30 students, 18 play football, and 12 of those also play tennis. Of the 12 students who do not play footba… - Interpreting a mean with a margin of error
A random sample of a town's households has a mean weekly grocery spend of 120 dollars, with a margin of error of 6 dolla… - Conclusion from a self-selected diet study
A researcher compared two groups of volunteers: those who had chosen a vegetarian diet and those who had not. The vegeta… - Effect of raising only the low scores on a mean
A class's test scores have a mean of 70, and at least one score is below 70. The teacher adds 10 points to every score t… - Probability of at least one of two events
For two events A and B, the probability of A is 0.5, the probability of B is 0.4, and the probability that both A and B … - Distribution of many sample means
A researcher draws 1,000 random samples of 50 adults each from a population and records the mean height of each sample. … - Comparing death rates at two hospitals
Hospital A has a death rate of 4 percent among its patients and Hospital B a rate of 2 percent. Hospital A is a speciali…
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