Problem-Solving and Data AnalysisHardEffect of removing an outlier
Problem-Solving and Data Analysis practice question
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 following is true?
- A. The mean decreases by more than the median decreases.Correct
- B. The median decreases by more than the mean decreases.
- C. The mean and the median decrease by the same amount.
- D. Neither the mean nor the median changes.
Answer: A. The mean decreases by more than the median decreases.
Mean: 70/5 = 14 before, 30/4 = 7.5 after — a drop of 6.5. Median: 8 before, (7 + 8)/2 = 7.5 after — a drop of 0.5. The mean is far more sensitive to the outlier.
Why the other answers are wrong
- B. The median decreases by more than the mean decreases.
- The median only moves from 8 to 7.5. The mean drops from 14 to 7.5.
- C. The mean and the median decrease by the same amount.
- They both end at 7.5, but they started at different places: mean 14, median 8.
- D. Neither the mean nor the median changes.
- Both change. Removing a value always changes the mean unless that value equals the mean, and 40 is far from it.
More Problem-Solving and Data Analysis questions
- Hard
The mean of five numbers is 12. If four of them are 8, 10, 14, and 16, what is the fifth number? - Hard
In a survey of 50 people, 30 like coffee, 20 like tea, and 8 like both. How many like neither? - Hard
A car travels at 60 mph for 2 hours, then 40 mph for 3 hours. What is its average speed for the whole trip? - Hard
Which statement correctly compares the standard deviations of the two sets? - Hard
Which statement best interprets the slope of the line of best fit? - Hard
How many milliliters of the 40% acid solution must the chemist add?
Not affiliated with the College Board. SAT is a trademark of the College Board.