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

Answer:

See Explanation

Step-by-step 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:

$M = \frac{N + 1}{2}$

For, the lower half:

$Q_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3rd$

So:

$Q_1 = 64$

For the upper half:

$Q_3 = \frac{5 + 1}{2} = \frac{6}{2} = 3rd$

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