For a class test, the mean score was , the median score was , and the standard deviation of the scores was . The teacher decided to add points to each score due to a grading error. Which of the following statements must be true for the new scores?
|I.||The new mean score is .|
|II.||The new median score is .|
|III.||The new standard deviation of the scores is .|
Select an Answer
, , and
For this type of question you need to evaluate each statement separately. Statement is true. If you add to each number in a data set, the mean will also increase by . Statement is also true. The relative position of each score will remain the same. Thus, the new median score will be equal to more than the old median score. Statement is false. Since each new score is 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.