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 $7$. $_\square$