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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 :-

Name
Time taken (In seconds)
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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