A relative frequency histogram is a histogram where we plot the relative frequencies on the y axis. The main difference between a relative frequency histogram and a regular histogram is that we plot the frequencies in a regular histogram whereas we plot the relative frequencies in a relative frequency histogram.

By relative frequency of a class interval, we mean the frequency of that interval expressed as a fraction of the total frequency. Therefore,

\text{Relative frequency} = \frac{\text{Given frequency}}{\text{Total Frequency}}**How to make a relative frequency histogram?**

- Given the grouped data, find the relative frequencies using the above formula and construct the relative frequency distribution table.
- Plot the class intervals on the X-axis.
- Plot the relative frequencies on the Y-axis.
- Draw the bars of the histogram with each bar having a height corresponding to its relative frequency.

**Example**:

A hundred students in a class gave a standardized test worth 40 marks. Construct the relative frequency histogram for the grouped data below:

Class Intervals | Frequency |

0-10 | 20 |

10-20 | 10 |

20-30 | 40 |

30-40 | 30 |

TOTAL=100 |

**Solution**: We first find the relative frequencies by dividing the frequencies by the total frequency (=100).

Marks obtained | Frequency | Relative Frequency |

0-10 | 20 | 20/100 = 0.2 |

10-20 | 10 | 10/100 = 0.1 |

20-30 | 40 | 40/100 = 0.4 |

30-40 | 30 | 30/100 = 0.3 |

TOTAL=100 |

Notice that the relative frequencies always add up to 1. We can also express the relative frequencies as percent by multiplying each relative frequency by 100. In that case, all the relative frequencies will add up to 100%. Now we construct the histogram by plotting the relative frequencies on the Y-axis.

**Use of Relative Frequency Histogram**:

Relative frequency is important because it tells us the chances of a particular outcome as a proportion of the total outcomes. The relative frequency histogram represents this information visually which then becomes much easier to grasp. Hence we can easily say what the probability of a particular outcome is based on the histogram. For example, from the histogram in the above image, we can conclude that there is a 40% chance that the student obtains marks between 20 and 30.