Question

You give a test to 100 students and determine the median of the scores. After grading the test you realize that the 10 students with the highest scores did exceptionally well. You decide to award these 10 students a bonus of 5 more points each. The median of the new score distribution will be (less than, greater than or the same as) that of the original score distribution?

Answer 1

R'>R

Explanation:

To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.

We know the range is defined by R

R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.

Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5. So, our range also becomes

R = X(n) + 5 - X(1)

So, R'>R. Hence, the range of the new score will be greater than that of the original score distribution.