Chapter 2.2, Problem 2.41E

(a)

To determine

To Calculate: the mean and median of the given data

Answer to Problem 2.41E

  $\mu =87.188$

Median = 87.5

Explanation of Solution

Given:

  $\begin{array}{l}\mu =69.188\\ \sigma =3.20\\ \text{Min}\text{. = 61}\text{.5}\\ {\text{Q}}_1=67.75\\ \text{Median = 69}\text{.5}\\ {\text{Q}}_3=71\\ \text{Max}\text{.=74}\text{.5}\end{array}$

Calculation:

Mean and median will be increased by 18 inches because it is affected by the constant increment.

Mean:

69.188+18=87.188

Median:

69.5+18=87.5

(b)

To determine

To Calculate: standard deviation and IQR of the given data.

Answer to Problem 2.41E

  $\begin{array}{c}\text{IQR}=3.25\\ \sigma =3.20\end{array}$

Explanation of Solution

Given:

  $\begin{array}{l}\mu =69.188\\ \sigma =3.20\\ \text{Min}\text{. = 61}\text{.5}\\ {\text{Q}}_1=67.75\\ \text{Median = 69}\text{.5}\\ {\text{Q}}_3=71\\ \text{Max}\text{.=74}\text{.5}\end{array}$

Formula used:

  ${\text{IQR=Q}}_3-{\text{Q}}_1$

Calculation:

  $\begin{array}{c}{\text{IQR=Q}}_3-{\text{Q}}_1\\ =71-67.75\\ =3.25\end{array}$

  $\sigma =3.20$ (Not affected by constant increase in height)