- From: Lynda O'Dea
- Date: 27 February 1999
*Subject: Frequency Density*
I'm doing GCSE Higher level. Can you explain what frequency density is? I keep seeing it in past exam papers but I'm sure we haven't done it in class. |

Frequency density needs to be calculated when drawing **histograms**, especially ones for
data with **unequal class widths**.

You will usually have the data in the form of a grouped frequency distribution, which is a table showing the data classes and the frequency (the number of data values) in each class.

First calulate the **width** of each class, which is the difference between the upper and
lower class bounds. Then calculate the **frequency density** of each class. This is calculated
by the formula:

This is best presented in a table. For example:

Time (mins) | Frequency | Class Width | Frequency Density |
---|---|---|---|

0 - 5 | 7 | 5 | 1.4 |

5 - 10 | 12 | 5 | 2.4 |

10 - 20 | 18 | 10 | 1.8 |

20 - 30 | 14 | 10 | 1.4 |

30 - 60 | 15 | 30 | 0.5 |

The histogram must be drawn by *plotting the frequency density* up the vertical axis:

The important thing about using the frequency density to plot the histogram is that **the
area of the bars will be equal to the actual frequency of the classes**.

Return to contents list