Five students take a test on which any integer score from 0 to 100 inclusive is possible. What is the largest possible difference between the median and the mean of the scores? (The median of a set of scores is the middlemost score when the data is arranged in increasing order. It is exactly the middle score when there are an odd number of scores and it is the average of the two middle scores when there are an even number of scores.)
Correct Answer: 40
Solution
With five scores the median is the third one. Taking the scores $$0, 0, 100, 100, 100$$ gives median 100 and mean 60, a difference of 40, while $$0, 0, 0, 100, 100$$ gives median 0 and mean 40, again a difference of 40. Pushing the two extreme scores to the ends is optimal, so the largest possible difference is 40.
Get AI Help
Book Free CAT Mentorship
Get personalized CAT strategy from a 99%iler
500+ students mentored
OTP Verification
Enter the 6-digit code sent to your phone
Booking Summary
Enter OTP
Didn't receive the OTP?
_1.webp)
