SAT Math · One-variable data: distributions and measures of center and spread · medium
A data set of 9 employee salaries has a median of $52,000. If the highest salary in the data set is replaced with a much larger value,…
A data set of 9 employee salaries has a median of $52,000. If the highest salary in the data set is replaced with a much larger value, what is the most likely effect on the mean and median?
Answer and explanation
Answer: B: The mean will increase, but the median will likely stay the same or change very little.
The mean uses every value, so replacing the highest salary with a much larger one raises the total and therefore the mean. The median is the middle value (the 5th of 9 in order), and replacing the largest value with an even larger one does not change which value is in the middle, so the median stays the same. That is choice B. Choice A is wrong because the two measures react differently. Choice C reverses the roles of the mean and median. Choice D ignores that the mean depends on every value. The mean is sensitive to outliers; the median is resistant.
More One-variable data: distributions and measures of center and spread questions
- Question 18 · mediumThe mean of 9 numbers is 42. A 10th number is added to the list, and the mean of all 10 numbers…
- Question 40 · mediumA data set consists of the values 12, 15, 18, 22, and 25. If the values 1 and 100 are added to the…
- Question 219 · mediumThe mean of 6 numbers is 40. If the number 10 is removed from the list, what is the mean of the…
- Question 220 · mediumA data set has a range of 25. If every value in the data set is multiplied by 3, what is the range…
- Question 221 · mediumA data set has a standard deviation of 4. If every value in the data set is multiplied by 3, what…
- Question 239 · mediumClass A has a mean test score of 78 with a standard deviation of 5. Class B has a mean test score…
Learn the method behind questions like this one
The SAT Math course teaches each tested skill through lessons, step-by-step solutions to sample problems, the complete study guide and full-length practice tests.