Question

In Mrs. Trainer's math class, Siobhan's first five math quiz scores are 76, 96, 81, 69, and 41. Siobhan takes the sixth math quiz and scores an 85. How will the mean change if the sixth score is added to the list?

Answer 1

the median will go up 2.5 points from 76 to 78.5

Explanation:

You want to know the effect on the median of adding 85 to the list of scores: 76, 96, 81, 69, 41.

Median

The median is the middle value when the list is sorted into order. The ordered list is ...

41, 69, 76, 81, 96

The median is 76.

New Median

When 85 is added to the list, the sorted list becomes ...

41, 69, 76, 81, 85, 96

There are two middle scores, so the median is their average:

(76+81)/2 = 78.5

The median increases 2.5 points from 76 to 78.5 when the score is added.