How to Find Mode in Statistics

What is mode in Statistics?

Mode is the data point that appears the maximum number of times in a data distribution. These numbers either belong to a sample data set or a population. The symbol ‘Mo’ represents the mode. In this article, we will see how to find Mode in Statistics.

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Is mode the same as the highest value?

No! Mode is neither the highest value in a data set nor does it have anything to do with the spread of the data.

It is concerned with the frequency of data points appearing in the given data set. Modes are the values in the data set that appear the maximum number of times.

Mode as a measure of central tendency

Mode is one of the primary measures of the central tendency of a data set, and the other two popular ones are mean and median. Measures of central location and summary statistics are some other names for measures of central tendency.

We use measures of central tendency to get more insights into the nature of the data set. The mode may not fall right in the middle of the data set, and it may not even represent the average value. Still, it captures the value of the data point occurring with a maximum frequency in the sample or population.

In many cases, there is no single suitable measure of central tendency to reveal everything about the nature of the data. In many cases, the mean or median represents the sample or population more accurately.

How to find mode in Math or Statistics?

Let us see how to calculate the mode of a data set.

Step 1

It is helpful to arrange the given data in ascending or descending order before calculating the mode.

Step 2

The mode is nothing but the values of the data points that repeat themselves the maximum number of times.

Note:

• If two or more values appear the maximum number of times, the data sets will have just as many modes.
• A distribution having one mode is called unimodal distribution. Multimodal distributions are data sets that have two or more modes.
• A bimodal distribution is a specific occurrence of multimodal distributions with two modes.

Solved problems

Example 1

What is the mode of the ungrouped sample data set containing 2, 4, 6, 2, 15, 13, 2, 14, 4, 16, 25, 2, and 20?

The data points in increasing order = 2, 2, 2, 2, 4, 4, 6, 13, 14, 15, 16, 20, 25

The data point occurring the maximum number of times = 2 (appears four times)

Mode = 2

Example 2

What is the mode of the ungrouped sample data set containing 3, 5, 6, 3, 15, 5, 13, 3, 14, 5, 16, 5, 25, 3, and 20?

The data points in increasing order = 3, 3, 3, 3, 5, 5, 5, 5, 6, 13, 14, 15, 16, 20, 25

The data point occurring the maximum number of times = 3 and 5 (both appear four times)

Mode = 3 and 5

The data set can have ungrouped or grouped data points. Unlike ungrouped data, we may not know the exact values of the data points in the sample or the population for grouped data. However, we know the frequency of the data points occurring in the groups or intervals. For such data, modes are the class intervals’ mid-point values with the highest frequency.

Example 3

The time (in minutes) taken by participants of a group to solve a set of puzzles is

18

24

17

26

13

33

31

34

8

21

21

11

21

17

11

21

14

15

25

20

 

Frequency distribution table of the time taken by the participants to solve a set of puzzles

Time taken (in minutes)	Frequency (fi)
1 ≤ t < 10	1
10 ≤ t < 15	4
15 ≤ t < 20	4
20 ≤ t < 25	6
25 ≤ t < 30	2
30 ≤ t < 35	3

 

Mode = l + [(f₁ – f₀) / (2f₁ – f₀ – f₂)] x h

 

In the given data, the maximum frequency is 6 for the modal class interval 20-25

l = lowest value in the modal class interval = 20

h = class interval size = 5

Also, f₀ = frequency of the class interval before the modal class interval = 4

f₁ = frequency of the modal class interval = 6

f₂ = frequency of the class interval after the modal class interval = 2

 

Mode = 20 + ((6-4) / (2 x 6 – 4 – 2)) x 5 = 21.67

 

How to find mode from a histogram

A histogram is a frequency table drawn as a bar chart. It is especially suited to easy calculation of mode as the longest/tallest bar(s) of the graph represents the mode. If the data is grouped, we need to follow the method illustrated in example 3.

How to find the mode in Excel

We use the native ‘MODE’ formula to find the mode in Excel. We select MODE from the formula dropdown menu containing formulas or type MODE in the formula bar. Then, we select the cells containing the data. For example, if we want to calculate the mode for column D, rows four through 21, the formula will be ‘MODE(D4:D21).

Refer to the blog posts ‘How to find mean‘ and ‘How to find median‘ in Statistics to learn how to calculate median and mode.

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