Question

James's weekly quiz scores are shown in the stem-and-leaf plot below.

If he drops his scores from the first two weeks, his mode score increases by $2$. How much would his mean score increase?

Answer 1

By 0.75

Explanation:

From the stem-and-leaf plot you can find James's scores:

79, 81, 83, 83, 83, 85, 85, 88, 94, 99.

The mode is 83 (most often score). If he drops his scores from the first two weeks, his mode score increases by 2. This means that the mode became 85 and the data looks like

79, 81, 83, 85, 85, 88, 94, 99.

Now find two means.

1. The old mean:

`(79+81+83+83+83+85+85+88+94+99)/(10)=(860)/(10)=86;`

2. The new mean:

`(79+81+83+85+85+88+94+99)/(8)=(694)/(8)=86.75;`

Thus, the mean will increase by 0.75.