Question

the scores for 21 students on an exam are summarized in the stemplot given.
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?
options:
neither the mean nor the median will change.
the mean and median will both increase.
the mean will increase but the median will be unchanged.
the mean will increase but the median will decrease.

Explanation:

Step1: List all original scores

Scores: 49, 69, 71, 72, 75, 75, 76, 77, 80, 81, 82, 84, 85, 85, 86, 89, 89, 90, 91, 94, 97

Step2: Calculate original median

Total data points: 21. Median is the 11th value: $82$

Step3: Calculate original sum of scores

$49 + 69 + 71 + 72 + 75 + 75 + 76 + 77 + 80 + 81 + 82 + 84 + 85 + 85 + 86 + 89 + 89 + 90 + 91 + 94 + 97 = 1690$

Step4: Correct the score and get new data

Change 49 to 69. New scores: 69, 69, 71, 72, 75, 75, 76, 77, 80, 81, 82, 84, 85, 85, 86, 89, 89, 90, 91, 94, 97

Step5: Calculate new median

11th value remains $82$ (unchanged)

Step6: Calculate new sum and mean

New sum: $1690 - 49 + 69 = 1710$. New mean: $\frac{1710}{21} \approx 81.43$, original mean: $\frac{1690}{21} \approx 80.48$. Mean increases.

Answer:

The mean will increase but the median will be unchanged.