College

Scores: 50, 70, 71, 72, 73, 72, 62, 72

What range of values describes the middle 50% of the scores?

A. 71 to 72
B. 66 to 72
C. 66 to 71
D. 66 to 71.5

Answer :

The middle 50% of values of the data set is the interquartile range (IQR).

The IQR is given by the formula:

[tex]IQR=Q3-Q1[/tex]

where Q1 is the 25th percent of values and Q3 is the 75th percent of values.

We can get the Q1 and Q3 values as shown below:

Therefore, the Q1 value will be:

[tex]Q1=\frac{62+70}{2}=66[/tex]

and the Q3 value will be:

[tex]Q3=\frac{72+72}{2}=72[/tex]

Therefore, the middle 50% of the scores are given from 66 to 72.

OPTION B is the correct option.