Question

A data set is made up of these values.

3, 3, 4, 5, 6, 7, 10
Find the interquartile range.
A. 3 - 3 = 0
B. 10 - 7 = 3
C. 7 - 3 = 4
D. 10 - 3 = 7

Answer 1

C. 7 - 3 = 4

Explanation:

Given

`Dataset: 3, 3, 4, 5, 6, 7, 10`

Required

The IQR

The IQR is calculated using:

`IQR = Q_3 - Q_1`

Where:

`Q_3 \to` Median of the upper
`half`

`Q_1 \to` Median of the lower
`half`

The dataset has 7 values, so the median is: (7 + 1)/2 =8/2 = 4th position.

Split to two, we have:

`Lower \to 3, 3, 4`

`Median \to 5`

`Upper \to 6, 7, 10`

The lower half has 3 data; So, the median is the 2nd position.

Hence:

`Q_1 = 3`

The upper half has 3 data; So, the median is the 2nd position.

Hence:

`Q_3 = 7`

So, the IQR is:

`IQR = Q_3 - Q_1`

`IQR = 7 - 3`

`IQR = 4`