Question

94, 73, 68, 83, 100, 68, these are the test scores.

The student takes 2 more 100 point tests Before the grading period closes. The addition of these 2 test scores has no effect on the mean, but the median score of all the tests increased by 2 points. What was the scores of the 2 most recent tests?

Answer 1

Explanation:

Thw two most recent score were 74 and 82

Answer 2

Here are the step-by-step workings to solve this problem:

The current test scores are: 94, 73, 68, 83, 100, 68

The student takes 2 more tests which have no effect on the mean, but increase the median by 2 points.

The mean of the current 6 test scores is (94 + 73 + 68 + 83 + 100 + 68)/6 = 82

Adding the 2 new test scores will keep the mean at 82, so the sum of the 2 new scores is 2x - 164, where x is the value of each test score.

The current median is (68 + 83)/2 = 76

Increasing the median by 2 points means the new median will be 78.

The 2 new test scores must be on either side of 78 to make it the median. Let's say one score is 74 and the other is 82.

Therefore, 74 + 82 = 156, which matches the sum found in step 4 (2x - 164 = 156, so x = 80).

So the two most recent test scores were 74 and 82, which satisfy the conditions that:

Their sum keeps the mean at 82

Their values increase the median by 2 points to 78

The key steps are determining the mean, finding the sum required to keep the mean the same, and then testing values that would increase the median by the given amount.