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Mode in Maths

Mode Meaning and Definition

In Statistics, the mode is a set of data or observations that occurs multiple times. The mode has the highest frequency of occurrence in the given set of data. The given set of data can have one mode or more than one mode, which means if two values are repeating with the same frequency then we call the mode of the given set of data. If a given set of data has one mode then it’s called unimodal, if it has two modes then it’s called bimodal, if it has three modes then it’s called trimodal, if the data has more than four or four modes then we called it multimodal.

Mode Formula in Statistics (Maths)

Let’s learn with the example, we have given an example below, where we have given the score of a cricket match along with the score we have given the number of balls. 

Number of Balls 1 2 3 4 5 6 7 8 9
Runs 1 2 4 6 2 1 4 6 4

 

In the above example, the number 4 is repeated 3 times and which is the highest frequency of the data given in the table. That means only number 4 repeated 3 times, no other number repeated 3 times. So, we have learned above the definition of mode, through the definition of mode the above example has only one mode which is 4, and the data which has only one mode is called unimodal.

Types of Mode in Maths/Statistics

There are four types of modes which are unimodal, bimodal, trimodal, and multimodal. Let us understand these modes with the help of an example: 

Unimodal Mode

If the set of given data or observations contains only one mode then this mode is known as a unimodal mode. 

Example: If the given set of data is X = { 2, 10, 14, 10, 12, 10, 8, 3, 2, 10, 2, 9}

In the data set 10 has the highest frequency then it can be called the unimodal data set. 

Bimodal Mode

If the set of given data or observations contains only two modes then this mode is known as a bimodal mode. 

Example: If the given set of data is X = { 2, 1, 2, 10, 1, 1, 8, 3, 2, 1, 2, 9}

In the data sets, 2 and 1 have the highest frequency then it can be called the bimodal data set. 

Trimodal Mode

If a data set or observation has three modes then it’s called trimodal mode. If the data set has 3 values that are repeating with the same frequency that you can say that the given data set has three modes. 

Example: If the given set of data is X = {11, 12, 11, 13, 10, 9, 12, 13, 8, 7, 1, 2, 4}

In the example above, the numbers 11, 12, and 13 are repeated with the same frequency and have the highest frequency among other numbers. Hence, it is called a trimodal data set. 

Multimodal Mode

If a given set of data has more than four or four modes is called multimodal mode. Let us understand multimodal mode with an example

Example: Given a set of data Y = {2, 3, 5, 1, 2, 5, 6, 7, 4, 3, 1, 4, 7}

The above example has 5 modes then these modes are called multimodal modes. All 5 modes are repeating with the same frequency. 

 

For Grouped Data Use the Mode Formula

It is not possible to calculate the mode of a grouped frequency distribution simply by looking at the frequency. In such instances, the modal class is used to calculate the mode of data. To calculate the mode for such data we have given the formula below use this formula and calculate the mode. 

Mode formula for continuous series

Mode = l+(f1-f0/2f1-f0-f2)*h

Where,

l = l is the lower limit of the modal class

h = size of the class interval

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeeding the modal class

 

How to Calculate the Mode in Maths/Statistics?

Here we have given examples to calculate the modes, solve these examples on your own and practice them for a better understanding of modes. 

Example 1: Calculate the mode of the given data set: 4, 1, 4, 2, 5, 6, 4, 1, 5, 8, 9

Solution:  In the following set of data {4, 1, 4, 2, 5, 6, 4, 1, 5, 8, 9}

4 is the highest repeating number as compared to other numbers, and it is repeating three times so we can call it trimodal mode. 

 

Example 2: Find the mode of 2, 4, 5, 11, 10, 6, 8, 9, 10, 7 data sets.

Solution: Given: 2, 4, 5, 11, 10, 6, 8, 9, 10, 7 is the data set.

In the given data set no number is repeating then we can say that the given data set does not contain any mode. 

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FAQs on the Mode in Maths

Q. What is the mode in statistics?

In Statistics, the mode is a set of data or observations that occurs multiple times. The mode has the highest frequency of occurrence in the given set of data. 

 

Q. How to find the mode for a given set of values?

If we have a set of values equal to 2, 4, 5, 6, 2, 7, 2. Then the most repeated value in the given set is 2. Therefore, the mode of the given set is 2.

 

Q. Can there be two modes in a given set of data?

Yes, a given set of data can contain two modes such modes are known as bimodal modes.

 

Q. What is the trimodal mode?

If a given set of data has three modes then these modes are known as a trimodal mode.

 

Q. What is multimodal mode?

If the given set of data has four or more than four modes then such modes are known as multimodal modes.

 

Q. What is no mode condition?

It is considered to be no mode if the given set of data has no value that is repeated in the set more than once.

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