### Mean when data set is presented in a frequency table

The following table gives the number of children in each of 20 families. Calculate the mean number of children per family.

#### Example 2

Number of children | 0 | 1 | 2 | 3 |
---|---|---|---|---|

Frequency | 4 | 5 | 7 | 4 |

#### Solution

There are 4 families with 0 children. This gives a total of 0 children.

There are 5 families with 1 child. This give a total of 1 × 5 = 5 children.

Continuing in this way, we have:

It is obviously impossible for a family to have 1.55 children, though this figure can be used by governments and other institutions for planning purposes. In general, the mean or average of a data set is not one of the original values.

### Mean when data is presented in a stem-and-leaf plot

#### Example 3

The stem-and-leaf plot below gives the marks of 12 students in a test.

1 | 8 | 9 | ||

2 | 2 | 4 | 5 | 6 |

3 | 1 | 4 | 9 | |

4 | 2 | 3 | 6 | |

4\(\mid\)3 means 43 |

Calculate the mean of the marks.

#### Solution

\begin{align}\text{Mean}\ &=\ \dfrac{18 + 19 + 22 + 24 + 25 + 26 + 31 + 34 + 39 + 42 + 43 + 46}{12}\\\\ &=\ \dfrac{369}{12}\\\\ &=\ 30.75\end{align}### Mean when data is presented in a column graph

#### Example 4

The marks obtained for a quiz by a group of students are displayed in the column graph.

Find the mean of the marks.