Question

the scores for 21 students on an exam are summarized in the stemplot below.

exam scores

4 | 9
5 |
6 | 9
7 | 1 2 5 5 6 7
8 | 0 1 2 4 5 5 6 9 9
9 | 0 1 4 7

key: 9|0 = 90% on the exam

the teacher realizes that a mistake was made and the student whose score was recorded as 49% should have been 69%. if the mistake is corrected, what effect will this have on the mean and median scores?

• the mean and median will both increase.
• neither the mean nor the median will change.
• the mean will increase but the median will decrease.
• the mean will increase but the median will be unchanged.

Explanation:

Step1: List all scores

Original scores: 49; 69; 71,72,75,75,76,77; 80,81,82,84,85,85,86,89,89; 90,91,94,97 (21 scores total).
Corrected scores: 69 replaces 49 → 69,69; 71,72,75,75,76,77; 80,81,82,84,85,85,86,89,89; 90,91,94,97.

Step2: Find median

21 scores → median = 11th score.
Original 11th score: 82.
Corrected 11th score: 82 (unchanged).

Step3: Analyze mean

Mean = total sum / 21.
Sum increases by 69-49=20 → mean increases.

Answer:

D. The mean will increase but the median will be unchanged.