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The most frequently occurring element in a set of data is called **mode**.

Let's understand the concept of mode.

Rose, Sherry, Olivia, Helen, and Betty took part in a race. The following table shows the time taken by them to complete the race :-

Rose

144

Oliva

156

Sherry

144

Betty

144

Helen

156

What is the mode of time taken ?

Here, we can see **Time taken by Rose is 144 seconds**

Time taken by Olivia is 156 seconds

**Time taken by Sherry is 144 seconds**

**Time taken by Betty is 144 seconds**

Time taken by Helen is 156 seconds

Since, 144 seconds is the time taken by 3 girls.

So, mode of the time taken by girls is "**144 seconds**"

**Example 1**

**Consider the following set: 2, 4, 5, 5, 7**

Let's see how many times each number appears in this set.

2 is appearing once

4 is appearing once

5 is appearing twice

7 is appearing once

The number that appears most often is 5.

So, 5 is the mode of the given data.

**Example 2**

**Consider another set: 1, 1, 1, 2, 2, 3, 4, 4, 4, 4.**

Let's find the frequency of each element of the given set where frequency is the number of times a particular element recurs in the set.

Frequency of 1 is 3

Frequency of 2 is 2

Frequency of 3 is 1

Frequency of 4 is 4

4 appears most often.

So, 4 is the mode.

Bimodal Data Set:

We can have more than one mode.

A set of data with 2 modes (i.e., two numbers that occur most often, and the same number of times) is called **bimodal**.

Let's illustrate through an example.

**Example 3**

**Test scores of 9 fourth graders are listed below.**

**24, 15, 18, 22, 18, 22, 24, 18, 24**

Let's find the frequency of each element of the given set where frequency is the number of times a particular element recurs in the set.

Frequency of 15 is 1

Frequency of 18 is 3

Frequency of 22 is 2

Frequency of 24 is 3

Since both 18 and 24 occur three times, the modes are 18 and 24. This data set is bimodal.

Summary

- The most frequently occurring element in a set of data is called mode.
- There can be more than one mode in a data set.
- Data set with two modes is called bimodal.

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