Chapter 11.5, Problem 3E

To determine

To calculate:

Population mean $\left(\mu \right)$ for the given sample.

Answer to Problem 3E

Population mean $\left(\mu \right)$ for the given sample is $60.4$ .

Explanation of Solution

Given information:

Number of text messages
$30$	$60$	$59$	$83$	$41$
$37$	$66$	$63$	$60$	$92$
$53$	$42$	$47$	$32$	$79$
$53$	$80$	$41$	$51$	$85$
$73$	$71$	$69$	$31$	$69$
$57$	$60$	$70$	$91$	$67$

Calculation:

Population mean is calculated as,

  $\mu =\frac{{\displaystyle \sum X}}{N}$

Where,

  $\mu =$ Population mean.

  $X=$ All the individuals items.

  $N=$ Total number of items.

Substitute the values in above equation,

  $\begin{array}{l}\mu =\frac{{\displaystyle \sum X}}{N}\\ \mu =\frac{30+37+53+53+73+57+60+66+42+80+\mathrm{.....}+67}{30}\\ \mu =\frac{1812}{30}\\ \mu =60.4\end{array}$

Hence, Population mean $\left(\mu \right)$ for the given sample is $60.4$ .