# Modal Class

## Modal Class

Class in which the frequency is the highest in a distribution of a continuous quantitative statistical variable in which the values are grouped into classes with the same dimensions.

The mode is rarely used as a measure of central tendency for continuous quantitative variables. The mode is more useful for qualitative variables because the mean and the median do not make sense.

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.