Question

The difference between the highest and lowest single game point totals for the MIDDLE HALF of the data is ______ points less for Joe's data than Sam's data. Therefore, the MIDDLE HALF of Joe's single game point totals are less varied than Sam's.

Answer 1

See Explanation

Explanation:

The question is incomplete, as the required data to answer the question are missing.

However, the interpretation of the question is to determine the interquartile range (IQR) of a certain dataset.

Then get the difference between the calculated IQR & Joe's data and also the difference between the calculated IQR & Sam's data

Then, make comparison

To do this, I will use the following assumed datasets.

`Data: 62, 63, 64, 64, 70, 72, 76, 77, 81, 81`

IQR is calculated as:

`IQR = Q_3 - Q_1`

`Q_3` is
`the\ median` of the upper half

`Q_1` is
`the\ median` of the lower half

For Joe, we have:

`Lower\ half: 62, 63, 64, 64, 70`

`Upper\ half: 72, 76, 77, 81, 81`

The median is then calculated as:

`M = (N + 1)/(2)`

For, the lower half:

`Q_1 = (5 + 1)/(2) = (6)/(2) = 3rd`

So:

`Q_1 = 64`

For the upper half:

`Q_3 = (5 + 1)/(2) = (6)/(2) = 3rd`

So:

`Q_3 = 77`

When the same process is applied to Sam's data,

`Q_1 = 52`

`Q_3 = 58`

`IQR = Q_3 - Q_1`

`IQR = 77 - 64`

`IQR = 13`

Assume that:

`Joe = 60`

`Sam = 65`

`Joe - IQR = 60 - 13 = 47`

`Sam- IQR = 65- 13 = 52`

Hence, the IQR is 47 points less for Joe's data than Sam's