A histogram is a chart consisting of bars to represent continuous grouped data.

The class intervals may be unequal and there are no gaps between the bars.

Frequency is proportional to the areas of the bars.

Frequency density = |
frequency |

width of class interval |

**Example**

A company has 725 workers

The following table shows the distribution of weekly wages.

Weekly Wages (£) | frequency (f) |
---|---|

0 ≤ w < 200 | 200 |

200 ≤ w < 300 | 200 |

300 ≤ w < 350 | 125 |

350 ≤ w < 500 | 150 |

500 ≤ w < 600 | 50 |

Total | 725 |

Work out the Frequency Densities for this distribution and draw a histogram to display this information.

**Answer**

We extend the table with two new columns to show class width and Frequency density.

Using the formula below, we work out the Frequency density for each class width.

Frequency density = |
frequency |

width of class interval |

Weekly Wages (£) | frequency (f) | Class width | Frequency density |
---|---|---|---|

0 ≤ w < 200 | 200 | 200 | 200 ÷ 200 = 1 |

200 ≤ w < 300 | 200 | 100 | 200 ÷ 100 = 2 |

300 ≤ w < 350 | 125 | 50 | 125 ÷ 50 = 2.5 |

350 ≤ w < 500 | 150 | 150 | 150 ÷ 150 = 1 |

500 ≤ w < 600 | 50 | 100 | 50 ÷ 100 = 0.5 |

Total | 725 |

**Weekly wages **are then plotted against **Frequency density** to produce the following histogram.

For this worksheet, you will need the formula:

Frequency = Frequency Density × Class Width