A relative frequency histogram is a histogram where we plot the *relative* frequency on the Y-axis. Normally when plotting a histogram we put the data values on the X-axis and the frequency on the Y-axis.

But we can also consider the relative frequency, that is the proportion of data values that lie within a category. If we plot the relative frequency instead of the actual frequency on the Y-axis, then the histogram so obtained is known as 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.

**Relative frequency = Given frequency/Total Frequency.**

**How to make a relative frequency histogram?**

- Given the grouped data, find the relative frequencies by dividing the frequency by the total frequency. 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 1: **

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.

**Example 2:**

Consider the following set of data values showing the Class intervals and the corresponding relative frequency.

We plot the relative frequencies on the Y-axis to create the relative frequency histogram.

Note that the height of a bar in a relative frequency histogram is always less than 1. Since the relative frequency is always less than or equal to 1, the maximum height of a bar in a relative frequency histogram is equal to 1.

**When do we use a Relative Frequency Histogram:**

We use a relative frequency histogram when we are interested in comparing the different categories. If we are only interested in comparing the categories then it is enough to know the proportion of data values that lie within each category. It is not necessary to know the absolute frequency in this case.

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 first example, we can conclude that there is a 40% chance that the student obtains marks between 20 and 30.

**Frequency Histogram vs Relative Frequency Histogram:**

The main difference between a frequency histogram and a relative frequency histogram is that in a regular histogram, we plot the frequencies on the Y-axis whereas in a relative frequency histogram, we plot the relative frequencies on the Y-axis.

Both of the histograms when actually plotted have the same shape and look exactly the same. The difference between them lies in the scale chosen for the Y-axis.