Chapter 1.3, Problem 106E

To determine

To calculate the interquartile range.

Answer to Problem 106E

Interquartile Range = 2.8

Explanation of Solution

Given:

Mean = 3.2

Standard deviation = 1.9

  

Calculation:

The first quartile is the median value of first 6 values,

  $\begin{array}{c}{\text{Q}}_{\text{1}}=\frac{15+17}{2}\\ =\frac{32}{2}\\ =16\end{array}$

Which means the value 16 that divides the dataset of first 6values in two equal parts

Similarly, the third quartile will be the median value of last 6 values which means that it should divide the last 6 values in two equal parts.

  $\begin{array}{c}{\text{Q}}_{\text{1}}=\frac{27+29}{2}\\ =\frac{56}{2}\\ =28\end{array}$

Therefore, the First quartile = 16

And, Third quartile = 28

  $\begin{array}{l}{\text{Interquartile Range = Q}}_3-{\text{Q}}_1\\ \text{= 28 - 16}\\ \text{= 12}\end{array}$