Chapter 11.5, Problem 4E

To determine

To calculate:

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

Answer to Problem 4E

Population mean $\left(\mu \right)$ for the given sample is $51029$ .

Explanation of Solution

Given information:

Income of U.S Households
$14300$	$52100$	$74800$	$51000$	$91500$
$72800$	$50500$	$15000$	$37600$	$22100$
$40000$	$65400$	$50000$	$81100$	$99800$
$43300$	$32500$	$76300$	$83400$	$24600$
$30800$	$62100$	$32800$	$21900$	$64400$
$53200$	$45500$	$55300$	$19100$	$63100$
$73100$	$20000$	$49700$	$71000$	$45900$
$53200$	$45500$	$55300$	$19100$	$63100$

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,

  $\begin{array}{l}\mu =\frac{{\displaystyle \sum X}}{N}\\ \mu =\frac{14300+72800+40000+43300+30800+73100+53200+52100+50500+65400+32500+\mathrm{....}+63100}{35}\\ \mu =\frac{1786000}{35}\\ \mu =51029\end{array}$

Hence, Population mean $\left(\mu \right)$ for the given sample is $51029$ .