In statistics, the **mode** is the value which is repeatedly occurring in a given set. We can also say that the value or number in a data set, which has a high frequency or appears more frequently is called mode or **modal value**. It is one of the three measures of central tendency, apart from mean and median.

For example, mode of the set {3, 7, 8, 8, 9}, is 8. Therefore, for a finite number of observations, we can easily find the mode. A set of values may have one mode or more than one mode or no mode at all.

**Table of Contents:**

## Definition

A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

**Example**: In the given set of data: 2, 4, 5, 5, 6, 7, the mode of the data set is 5 since it has appeared in the set twice.

Statistics deals with the presentation, collection and analysis of data and information for a particular purpose. To represent this data, we use tables, graphs, pie-charts, bar graphs, pictorial representation and so on. After the proper organization of the data, it must be further analyzed to infer some useful information from it.

For this purpose, frequently in statistics, we tend to represent a set of data by a representative value which would roughly define the entire collection of data. This representative value is known as the measure of central tendency. By the name itself, it suggests that it is a value around which the data is centred. These measures of central tendency allow us to create a statistical summary of the vast organized data. One such measure of central tendency is the mode of data.

**Example**: In the given set of data: 2, 4, 5, 5, 6, 7, the mode of the data set is 5 since it has appeared in the set twice.

## Bimodal, Trimodal & Multimodal (More than one mode)

- When there are two modes in a data set, then the set is called
**bimodal**

For example, The mode of Set A = {2,2,2,3,4,4,5,5,5} is 2 and 5, because both 2 and 5 is repeated three times in the given set.

- When there are three modes in a data set, then the set is called
**trimodal**

For example, the mode of set A = {2,2,2,3,4,4,5,5,5,7,8,8,8} is 2, 5 and 8

- When there are four or more modes in a data set, then the set is called
**multimodal**

**Also, read:**

## Mode in Maths

The value occurring most frequently in a set of observations is its mode. In other words, the mode of data is the observation having the highest frequency in a set of data. There is a possibility that there exists more than one observation having the same frequency, i.e. a data set could have more than one mode. In such a case, the set of data is said to be multimodal.

Let us look into an example to get a better insight.

**Example: The following table represents the number of wickets taken by a bowler in 10 matches. Find the mode of the given set of data.**

It can be seen that 2 wickets were taken by the bowler frequently in different matches. Hence, the mode of the given data is 2.

## Mode Formula

In the case of grouped frequency distribution, calculation of mode just by looking into the frequency is not possible. To determine the mode of data in such cases we calculate the modal class. Mode lies inside the modal class. The mode of data is given by the formula:

Where,

l = lower limit of the modal class

h = size of the class interval

f_{1} = frequency of the modal class

f_{0} = frequency of the class preceding the modal class

f_{2} = frequency of the class succeeding the modal class

Let us take an example to understand this clearly.

## Finding the Mode

Let us learn here how to find the mode of a given data with the help of examples.

**Example 1: Find the mode of the given data set: 3, 3, 6, 9, 15, 15, 15, 27, 27, 37, 48.**

Solution: In the following list of numbers,

3, 3, 6, 9, 15, 15, 15, 27, 27, 37, 48

15 is the mode since it is appearing more number of times in the set compared to other numbers.

**Example 2: Find the mode of 4, 4, 4, 9, 15, 15, 15, 27, 37, 48 data set**.

Solution: Given: 4, 4, 4, 9, 15, 15, 15, 27, 37, 48 is the data set.

As we know, a data set or set of values can have more than one mode if more than one value occurs with equal frequency and number of time compared to the other values in the set.

Hence, here both the number 4 and 15 are modes of the set.

**Example 3: Find the mode of 3, 6, 9, 16, 27, 37, 48.**

Solution: If no value or number in a data set appears more than once, then the set has no mode.

Hence, for set 3, 6, 9, 16, 27, 37, 48, there is no mode available.

## Mode of Grouped Data

**Example 4**: **In a class of 30 students marks obtained by students in mathematics out of 50 is tabulated as below. Calculate the mode of data given.**

Solution:

The maximum class frequency is 12 and the class interval corresponding to this frequency is 20 – 30. Thus, the modal class is 20 – 30.

Lower limit of the modal class (l) = 20

Size of the class interval (h) = 10

Frequency of the modal class (f_{1}) = 12

Frequency of the class preceding the modal class (f_{0}) = 5

Frequency of the class succeeding the modal class (f_{2})= 8

Substituting these values in the formula we get;

## Mean Median Mode Comparison

Mean |
Median |
Mode |

Mean is the average value that is equal to the ration of sum of values in a data set and total number of values.
Mean = Sum of observations/Number of observations |
Median is the central value of given set of values when arranged in an order. |
Mode is the most repetitive value of a given set of values. |

For example, if we have set of values = 2,2,3,4,5, then; |
||

Mean = (2+2+3+4+5)/5 = 3.2 |
Median = 3 |
Mode = 2 |

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How to calculate mode when modal class is the 1st class interval itself?