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

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

The mean household income for all three regions combined together is 55 (in \$1000).

#### Further Reading

- Five Number Summary Calculator
- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators