# 6.6 Calculating the mode

The final type of average to look at is the mode, which is the most common value in a data set. There can sometimes be more than one mode, which occurs when two or more values are equally common. Sometimes there will be no mode as each data value occurs only once. When you calculate the mode you will always find that it is one of the values in your original data set. The mode is also called the modal value.

## Example: Finding the mode 1

What is the mode of the following numbers?

3, 7, 5, 6, 4, 5, 6, 5, 7, 5

First group the same numbers together by listing them in size order:

3, 4, 5, 5, 5, 5, 6, 6, 7, 7

It is then easy to identify the modal value as 5 as this number occurs the most.

**Note**: To remember how to calculate this average use *Mode = Most*.

## Example: Finding the mode 2

What is the mode of the following amounts of money?

£8.99 £16.45 £17.50 £36.20 £6.75 £9.35 £12.99 £8.95

First list them in size order from lowest amount to highest:

£6.75 £8.95 £8.99 £9.35 £12.99 £16.45 £17.50 £36.20

You can now see that there is no mode (or modal value) as each amount of money occurs only once.

## Example: Finding the mode 3

Below is a set of data showing the number of people attending a yoga class each week over a year. What is the mode?

17 17 13 16 18 15 12 16 16 17 18 13

First list them in size order from lowest amount to highest:

12 13 13 15

__16 16 16____17 17 17__18 18

You can now see that two numbers occur the same number of times. 16 and 17 both occur three times, so in this set of data there are two modes or modal values – 16 and 17.

## Example: Finding the mode 4

To find the mode from a frequency table you need to find the value with the highest frequency. The results of a survey on a block of flats are shown in the frequency table below. The highest frequency, which can be seen in the ‘Number of flats’ column, is 18. This means that the mode or modal number of occupants is 3.

### Table 24

Number of occupants | Number of flats |

0 | 2 |

1 | 9 |

2 | 13 |

3 | 18 |

4 | 6 |

## Activity 15: Calculating the mode

Now calculate the mode of the following:

- 3, 6, 5, 7, 3, 5, 6, 6, 3, 4, 9, 6
- 13, 19, 11, 28, 17, 29, 16, 24, 15, 18
- 81 cm, 53 cm, 74 cm, 62 cm, 53 cm, 70 cm, 81 cm, 74 cm, 42 cm, 90 cm
- The table below shows the number of tries scored by a school rugby team during one month. What is the modal number of tries scored?

### Table 25(a)

Number of tries | Frequency |

0 | 5 |

1 | 8 |

2 | 6 |

3 | 3 |

### Answer

First list them in size order from lowest amount to highest:

3, 3, 3, 4, 5, 5, 6, 6, 6, 6, 7, 9

It is then easy to identify the modal value as 6 as this number occurs the most.

First list them in size order from lowest amount to highest:

11, 13, 15, 16, 17, 18, 19, 24, 28, 29

You can now see that each value occurs only once so there is no mode/modal value.

First list them in size order from lowest amount to highest:

42 cm, 53 cm, 53 cm, 62 cm, 70 cm, 74 cm, 74 cm, 81 cm, 81 cm, 90 cm

You can now see that three numbers occur the same number of times. 53 cm, 74 cm and 81 cm occur twice, so in this set of data there are three modes or modal values.

- To find the mode you need to look for the highest frequency in the table. In this case it is 8 which shows that the modal number of tries scored is 1.

#### Table 25(b)

Number of tries | Frequency |

0 | 5 |

1 | 8 |

2 | 6 |

3 | 3 |