Chapter 12.3, Problem 32STP

a)

To determine

To Evaluate: -mean and median for region.

Answer to Problem 32STP

  $2288$

Explanation of Solution

Given information :

Income per capita of $12$ states in a region of country.

Calculation :

  $\begin{array}{l}\text{Income Per Capita}\\ \begin{array}{ccc}\text{\$}\text{25778}& \text{\$}\text{25698}& \text{\$}\text{25200}\\ \text{\$}\text{23858}& \text{\$}\text{25580}& \text{\$}27828\\ \text{\$}29173& \text{\$}22861& \text{\$}32903\\ \text{\$}27870& \text{\$}27124& \text{\$}23995\end{array}\\ Mean=\frac{zpercapitaincome}{12}=\frac{317863}{12}\\ Mean=\text{\$}26488\\ Median=\frac{25580+22861}{2}=24220\\ Difference(26488-24220)=2288\end{array}$

b)

To determine

To Find: - standard deviation of the data round to nearest hundredth.

Answer to Problem 32STP

  $26197$

Explanation of Solution

Calculation :

  $\begin{array}{l}\sigma =\sqrt{\frac{\Sigma (x_i-\mu )}{N}},where\text{ µ is mean, N = 12}\\ $ {\text{(25778}-26488\text{)}}^{\text{2}}+{(23858-26488)}^2+{(29173-26488)}^2$$ +{\text{(27870}-26488\text{)}}^{\text{2}}+{(25698-26488)}^2+{(25580-26488)}^2$$ +{\text{(22861}-26488\text{)}}^{\text{2}}+{(27124-26488)}^2+{(25200-26488)}^2$=\underset{\_}{+{\text{(27828}-26488\text{)}}^{\text{2}}+{(32903-26488)}^2+{(23995-26488)}^2}\\ 12\\ =\frac{823571}{12}=68630\\ \sigma =\sqrt{\frac{\Sigma {(x_i-\mu )}^2}{N}}=\sqrt{68630}=261.97\end{array}$

c)

To determine

From are mean and median for region affected ?

Answer to Problem 32STP

Both will increases

Explanation of Solution

Given information :

State reported $\$22861$ is incorrect, and it was actually $\$24861.$

Calculation :

Mean will increase.

Since, difference between $(24861-22861)=\$2000$

Mean = $\frac{317863+2000}{12}=\$26655.25$

Median, will change at increases.

  $=\frac{25580+24861}{2}=25220.5$