A **histogram** is a specialized form of a bar chart. Data on a histogram is grouped together, with the groups being collected in specific ranges known as **class intervals**.

On a bar chart, the height of the bar gives the frequency. On a histogram, the *area* of the bar represents the frequency, rather than the height.

The height of each histogram bar is calculated by dividing the frequency by the **class Width**. This height is called the **Frequency Density**. Where the class intervals are all the same, the height of the chart is in direct proportion to the frequency.

The speed of cars passing a point on the road was recorded over a period of one hour. The data was plotted on a histogram. From the histogram, below, determine the number of cars that were driving between 20mph and 40mph.

The width of the class interval is 20 (10mph).

The frequency density for 20 < s ≤ 40 is 0.9

0.9 x 20 = 18 cars

Answer: 18 cars

The table below shows the amount that customers spent at a local shop. A histogram is to be plotted for this data. What is the value of frequency density for the class interval £0 < S ≤ £5?

Amount | Frequency |

0 < h ≤ 5 |
48 |

5 < h ≤ 10 |
32 |

10 < h ≤ 15 |
15 |

15 < h ≤ 20 |
17 |

20 < h ≤ 25 |
8 |

25 < h ≤ 30 |
4 |

The frequency for this class is 48.

The class interval is 5.

Frequency density = `frac(text(frequency))(text(class interval))` = 48 ÷ 5 = 9.6

Answer: 9.6

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