# Growing families

What do these statistics about family size mean?

## Problem

The table shows some information about family sizes.

Number of children | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

Number of families | 6 | 13 | 9 | 4 | 1 |

Find:

a) the mean number of children in a family

b) the mean number of siblings that each child has

*If you liked this problem, you might also like the longer problem it is based on, The Wrong Stats*

## Student Solutions

a) To find the average number of children per family, we need to know the total number of children, and divide this by the total number of families.

Number of children | 1 | 2 | 3 | 4 | 5 | total |
---|---|---|---|---|---|---|

Number of families | 6 | 13 | 9 | 4 | 1 | 33 |

Total number of children in families this size |
1$\times$6 = 6 |
2$\times$13 = 26 |
3$\times$9 = 27 |
4$\times$4 = 16 |
5$\times$1 = 5 |
80 |

80$\div$33 = 2.42

b) To find the average number of siblings, we need to know the total number of siblings of all of the children combined, and divide this by the total number of children.

Number of children | 1 | 2 | 3 | 4 | 5 | total |
---|---|---|---|---|---|---|

Number of families | 6 | 13 | 9 | 4 | 1 | |

Total number of children in families this size |
1$\times$6 = 6 |
2$\times$13 = 26 |
3$\times$9 = 27 |
4$\times$4 = 16 |
5$\times$1 = 5 |
80 |

Number of siblings each child in this size family has |
0 | 1 | 2 | 3 | 4 | |

Total number of siblings in families this size |
0$\times$6 = 0 |
1$\times$26 = 26 |
2$\times$27 = 54 |
3$\times$16 = 48 |
4$\times$5 = 20 |
148 |

148$\div$80 = 1.85