Question

$28$27$26$25$32$26$30$25$30$28$28$30The range of the data is , and the interquartile range is .

Answer 1

The Solution:

Given the data below:

28, 27, 26, 25, 32, 26, 30, 25, 30, 28, 28, 30.

Required:

To find the range and the interquartile range.

Step 1:

Arrange the given data in ascending order.

25, 25, 26, 26, 27, 28, 28, 28, 30, 30, 30, 32

The range is the difference between the smallest number and the largest number.

`Range=32-25=\text{\$}7.00`

Step 2:

Find the interquartile range.

`\begin{gathered} interquartile=Q_3-Q_1 \\ \text{ Where} \\ Q_3=\text{ median of upper half=\lparen}(3)/(4)*12)^(th)=9^(th)=30 \\ \\ Q_1=\text{median of lower half=\lparen}(1)/(4)*12)^(th)=3^(th)=26 \end{gathered}`

So,

`\text{ Interquartile}=Q_3-Q_1=30-26=\text{\$}4`

Therefore, the correct answers are:

Range = $7.00

Interquartile range = $4.00