# Mode Definition and Examples

The no or value in a data set, that appears more frequently or has a high frequency, is called mode or modal value.

In statistics, the value that is repeatedly occurring in a given set of nos is known as the mode.

It is 1 of the 3 measures of central tendency, apart from median and mean.

For instance, the mode of the given set {8, 7, 8, 3, 9}, is 8.

A set of values might have 1 mode or more than 1 mode or 0 mode at all.

Thus, for a finite no of observations, one can easily find out the mode.

## Definition

The value that has a higher frequency in a given set of nos is known as the mode.

Mode is the value that appears the most no of times.

For instance: In the given set of data of numbers: 2, 4, 5, 5, 6, 7, the mode of the data set is 5. This is because it has appeared in the set two times.

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

Bimodal is when there are 2 modes in a data set of values.

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

Trimodal is when there are 3 modes in a given data set of values.

For instance, consider the given data set of values = {2,2,2,3,4,4,5,5,5,7,8,8,8}. It’s mode is 8, 5 and 2.

Multimodal is when there are 4 or more than 4 modes in a given data set of values.

## Mode Formula in Ungrouped Data

The mode of the given data is the observation having the most or the greatest frequency in a given set of data.

In other words, the value occurring most frequently in a given set of observations is the mode of the given data set values.

There is a possibility that more than 1 observation has 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.

For instance: The table that follows represents the no of wickets taken by a bowler in ten matches. Find the mode of this data set values.

It can be observed that two wickets were taken by the bowler frequently in different matches.

Therefore, the mode of the given data set of values is two.

## Mode Formula For Grouped Data

To determine the mode of data in cases of grouped data, you calculate the modal class. You should know that the mode lies inside the modal class. The mode is calculated by the formula that follows:

## Formula

The mode calculation only by looking into the frequency is not possible in the case of grouped frequency distribution.

f2 = frequency of the class that succeeds the modal class
f0 = frequency of the class that precedes the modal class
f1 = frequency of the modal class
h = size of the class interval
l = lower limit of the modal class

## How To Find The Mode

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

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.

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.

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.

## Mean Median Mode Formula

There exists an important relationship between mean, median, and mode.

This can be expressed using the below – mentioned formula:

Mode = 3 × Median – 2 × Mean

## What is 0 (zero) mode or no mode condition?

If the given set of numbers or observations do not have any number or value that is repeated in the set, more than one time, then it is known to be 0 (zero) mode or no mode.

## What is trimodal and multimodal mode?

If there are 4 or greater than 4 modes, then it is known as multimodal mode.

If there are 3 modes in a given set of nos or data set, then it is known as trimodal.

## Can there be 2 modes in a given set of nos?

Yes, there can be 2 modes in a given set of numbers.

Such values are called bimodal.

## How to find mode for given set of values?

For instance, if you have a set of values = 33,44,55,55,66.

Then the most repeated value in the given nos is 55.

Therefore, mode of the given set of nos is 55.

## What is mode in statistics?

A mode, in statistics, is defined as the value that has greater frequency in the given set of nos.

It is the value that appears the most no of times.