For a class test, the mean score was 65, the median score was 71, and the standard deviation of the scores was 7. The teacher decided to add 5 points to each score due to a grading error. Which of the following statements must be true for the new scores? I.

II.

The new mean score is 70. The new median score is 76. III.

The new standard deviation of the scores is 12. (a) None (b) I only (c) II only (d) I and II only (e) I, II, and III

Correct Answer: D

Explanation:

For this type of question you need to evaluate each statement separately. Statement I is true. If you add 5 to each number in a data set, the mean will also increase by 5. Statement II is also true. The relative position of each score will remain the same. Thus, the new median score will be equal to 5 more than the old median score. Statement III is false. Since each new score is 5 more than the old score, the spread of the scores and the position of the scores relative to the mean remain the same. Thus, the standard deviation of the new scores is the same as the standard deviation of the old scores.