Problem-Solving and Data AnalysisHardCombined mean of two groups
Problem-Solving and Data Analysis practice question
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 mean score of all 30 students?
Answer: 84
A mean of all 30 needs the total of all their scores. Class 1 contributed 10 × 80 = 800 points and class 2 contributed 20 × 86 = 1,720. Together: 2,520 points over 30 students = 84.
Common wrong answers
- If you answered 82
- 82 would come from weighting the classes the wrong way round. The class of 20 has more weight, so the overall mean is closer to 86 than to 80.
- If you answered 83
- 83 is the average of the two means, (80 + 86) / 2. That would be right only if the classes were the same size. The larger class counts twice as much, pulling the overall mean toward 86.
- If you answered 86
- 86 is the mean of the larger class alone. The 10 students who averaged 80 lower the overall mean.
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.