The mode is one of the measures of location besides the mean, median, and quartiles. It can be applied to data at nominal scale or higher. Given a set of data at nominal scale or higher, its mode is that value which occurs with the highest frequency, i.e. it is the most common value. Stated another way, it is the value which occurs most frequently.

**Example 1**

In class, there are 30 and 10 male and female students, respectively. Since there are more males than females, we can conclude that the mode of the sex of the students is **male**.

**Example 2**

The following is a list of 7 kindergartners with their favorite colors.

The mode of the favorite colors is **red**, because red appears most frequently in the data set.

**Example 3**

Below are the scores of a math test achieved by a group students.

76 47 56 42 78 80 76 76 45 78 76 76 80 95 80

The data have two modes, that is **76** and **80**. Each of them appears 3 times, while the others appear less than 3 times.

As Example 3 demonstrates, it is possible that a data set has more than one mode. The data set in Example 3 is * bimodal*, meaning that it has two modes. If a data set has only one mode, it is said to be

*.*

**unimodal**

How to calculate the mode if the data is presented in a frequency distribution table? Apply the formula below.

where

L_{1} = the lower class boundary (LCB) of modal class, i.e. the class with the highest frequency

Δ_{1} = the difference between the frequency of the modal class and the frequency of next lower class

Δ_{2} = the difference between the frequency of the modal class and the frequency of next higher class

c = the width of the modal class

Mo =the mode

**Example 4**

The frequency distribution table below shows the employees’ monthly expenditure on mobile phone telecommunication. Find the mode.

**Answer**

The class with the highest frequency is the third class with the class interval 176-210. This class is the modal class. Its class width is c = 210.5 – 175.5 = 35 and its lower class boundary is L_{1} = 176 – 0.5 = 175.5. Furthermore, Δ_{1} = 20 – 13 = 7 and Δ_{2} = 20 – 7 = 13. Consequently, the mode of the data is as follows.

The mode of the employees’ monthly expenditure on mobile phone telecommunication is IDR 187,750.

**References**

Lind, D.A., W. G. Marchal, S. A. Wathen, Statistical Techniques in Business and Economics 10th Ed., McGraw-Hill Irwin, 1999

Shukla, M. C., S. S., Gulshan, Elements of Statistics for Commerce Students, S. Chand&Co.(Pvt) Ltd., 1971

Spiegel, M. R., Theory and Problems of Statistics, McGraw-Hill Inc., 1981