To calculate the mode of a distribution of grouped data, we can use the middle of the range (or the amplitude) of the modal class. The formula provided below gives a more precise theoretical value, if necessary.

### Formula

The mode of a distribution of grouped data is calculated by considering the frequency of the modal class and the preceding and following classes.

The formula is: \(Mod = L_{Mod} + \left( \dfrac{d_1}{d_1 + d_2} \right) a\) where

- \(L_{Mod}\) is the lower limit of the modal class
- \(d_1\) is the difference between the frequency of the modal class and the frequency of the preceding class
- \(d_2\) is the difference between the frequency of the modal class and the frequency of the following class
- \(a\) is the amplitude of the modal class

### Example

In the distribution represented by this bar graph, the modal class is the class determined by the bounds A and B, which is the class [48, 51[. It’s the class in which the frequency is the highest.

To calculate the mode of the modal class [48, 51[, we have:

- \(L_{Mod}\) = 48
- \(d_1\) = 9
- \(d_2\) = 12
- \(a\) = 3

The modal mode is given by: \(Mod = 48 + \left( \dfrac{9}{9 + 12} \right) × 3\), which is equal to 49.3 to the nearest tenth. This is close enough to the central value of the modal class, which is 49.5.