¶ 2019 AMC8 Problem 10
¶ nan
Problem:
The diagram shows the number of students at soccer practice each weekday during last week. After computing the mean and median values, Coach discovers that there were actually participants on Wednesday. Which of the following statements describes the change in the mean and median after the correction is made?
Answer Choices:
A. The mean increases by and the median does not change.
B. The mean increases by and the median increases by .
C. The mean increases by and the median increases by .
D. The mean increases by and the median increases by .
E. The mean increases by and the median increases by .
Solution:
The original values in increasing order are , and thus the median (middle) value is . After replacing one of the with , the new values are , with a median of . Therefore the median value increases by .
An increase of in the number of participants on one day is equivalent to an increase of participant per day. Therefore the mean (average) value increases by . (The mean values could also be directly computed. The mean is for the original set of values and after the mistake has been corrected.)
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions