THE MODE

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

L₁ = the lower class boundary (LCB) of modal class, i.e. the class with the highest frequency

Δ₁ = the difference between the frequency of the modal class and the frequency of next lower class

Δ₂ = 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 L₁ = 176 – 0.5 = 175.5. Furthermore, Δ₁ = 20 – 13 = 7 and Δ₂ = 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