# Mode

Mode is that observation in a frequency distribution which occurs the maximum times in the frequency distribution, or technically speaking, which has the highest frequency. Mode is derived from the French word *La Mode* which means fashion. A frequency distribution may have one or more than one modes. The distribution having only a single mode is called unimodal frequency distribution and the distribution having two modes is called bi-modal frequency distribution. Here are some formulas for calculating mode:

**Individual Series:**Just check out the maximum number of times an individual observation occurs.**Discrete Series:**Just check out the highest frequency of the observations.**Continuous Series:**The formula is

$l+\frac{f_{1}-f_{0}}{2f_{1}-f_{2}-f_{0}}h,$

where

- $l$ represents the lower limit of the modal class;
- $f_{1}$ represents the frequency of the modal class;
- $f_{2}$ represents the frequency of the class interval succeeding the modal class;
- $f_{0}$ represents the frequency of the class interval preceding the modal class;
- $h$ represents the width of the class interval.

For example, if the class interval is $30-40$, then its

- Lower Limit: $30$
- Width: $40-30=10$
- Upper Limit: $40$.

For more information on different types of series, see Statistical Series.

**Merits**:
Mode is easy to calculate and understand. In some cases, it can be located merely by inspection. It can also be estimated graphically from a histogram.
Mode is not at all affected by extreme observations.
It can be conveniently obtained in the case of open end classes.

**Demerits**:
Mode is not rigidly defined.
From the modal values and the sizes of two or more series, we cannot find the mode of the combines series.

## What is the mode of the following distribution: $1,2,3,3,4,4,4,5,5,6,6,7,7,7,7,8,8,9?$

Mode is the observation that occurs the most in a frequency distribution. Since $7$ occurs the most number of times in this distribution, thus the mode is $7$. $_\square$