# Solved (Free): Random samples of households were selected from each of three regions in a large metropolitan area. The number of households selected from

#### ByDr. Raju Chaudhari

May 31, 2021

Random samples of households were selected from each of three regions in a large metropolitan area. The number of households selected from each region and the corresponding mean household incomes are provided in the table below.

Region Households Selected (Number) Mean Household Income (\$1,000) A 75 49 B 30 80 C 20 40 What is the mean household income for all three regions combined? #### Solution Given that sample sizes (households selected numbers) are$n_1=75$,$n_2=30$,$n_3=20$. The mean household incomes (in \$1000) are $\overline{x}_1=49$, $\overline{x}_2=80$ and $\overline{x}_3=40$.

The mean household income for all three regions combined is

 \begin{aligned} \overline{X} &=\frac{n_1\overline{x}_1+n_2\overline{x}_2+n_3\overline{x}_3}{n_1+n_2+n_3}\\ &=\frac{75*49 + 30*80+20*40}{75+30+20}\\ &= 55 \end{aligned}