In this section we revisit the three types of average, the *mean*, *median* and *mode*. We also use the *range* of a set of data.

Mean | = | |

Median | = | middle value (when the data is arranged in order); where there are two central values, the median is their mean |

Mode | = | most common value |

Range | = | difference between largest and smallest values |

1 | 7 | 8 | 2 | 3 | 6 | 5 | 10 | 3 |

For this sample,

(a)

calculate the *mean*,

Mean = = = 5

(b)

determine the *median*,

To find the median, first write the numbers in order.

1 | 2 | 3 | 3 | 5 | 6 | 7 | 8 | 10 |

Median |

As the number of data items is odd, the median will be the middle number, which is 5 in this case, so

Median = 5

(c)

state the *mode*,

The mode is the most common value, which is 3 for this set of values.

(d)

calculate the *range*.

Range = 10 – 1 = 9

Determine the *median* of the following set of values:

44 | 32 | 88 | 19 | 33 | 74 | 62 | 31 | 33 | 56 |

First write the numbers in order:

19 | 31 | 32 | 33 | 33 | 44 | 56 | 62 | 74 | 88 |

In this case, there are 2 middle numbers, 33 and 44. The median will be the mean of these.

Median = = = 38.5

A class collected data on the number of people living in their home, which is shown in the following table:

Number of PeopleLiving in Home | Frequency |
---|---|

2 | 3 |

3 | 9 |

4 | 10 |

5 | 2 |

6 | 3 |

7 | 1 |

8 | 1 |

9 | 0 |

10 | 1 |

(a)

Calculate the *mean* number of people living in each home.

The first step is to complete the table below:

Number of PeopleLiving in Home | Frequency | Number of People × Frequency |
---|---|---|

2 | 3 | 6 |

3 | 9 | 27 |

4 | 10 | 40 |

5 | 2 | 10 |

6 | 3 | 18 |

7 | 1 | 7 |

8 | 1 | 8 |

9 | 0 | 0 |

10 | 1 | 10 |

TOTALS | 30 | 126 |

Mean = = 4.2 people per home

(b)

Determine the *median* of the data.

As there are 30 values, the median is the mean of the 15th and 16th values.

From the first table we can see that both the 15th and 16th values are 4, so the median is 4 people per home.

(c)

State the *mode* of the data.

The most common value is 4 so the mode is 4 people per home.