Mode Definition

The number/digit which frequently appears in a set of numbers/digits is called the mode. It refers to the value or number that appears most commonly in a given set of digits.

Examples

Example 1:

X = {7, 2, 3, 10, 7, 7, 3, 7}

In the above set X, the mode is 7 because it appears four times more than the other values.

Example 2:

Y = {2, 1, 8, 3, 4, 7, 5, 5, 9}

In the above set Y, the mode is 5 because it counted two times more than the other values.

Types of mode

The following are the different types of modes.

• Unimodal

It consists of a single mode. For example, in {2, 1, 3, 7, 11, 2, 5} only a single mode exists, which is 2.

• Bimodal

If a set of numbers have two modes, it is called Bimodal. For example, in {2, 9, 1, 3, 3, 5, 6, 7, 5} there are two modes, which are 3 and 5.

For example,

 In {2, 9, 1, 3, 3, 5, 6, 7, 5} there are two modes, which are 3 and 5.
• Trimodal

If a set of digits consists of three modes, it is called Trimodal. For example, in {2, 3, 3, 5, 6, 7, 5, 9, 9} there are three modes, which are 3, 5, and 9.

• Multimodal

If a set of digits consists of multiple modes, it is called multimodal.

For example,

 In {2, 3, 5, 2, 4, 4, 6, 1, 10, 1, 3, 7, 7} four modes exists.

The rules of finding a mode in a set of digits

We use the following rules to find a mode:

• Collect the set of digits.
• For easy counting, arrange the digits in the order form (Ascending or Descending).
• Now, count the digits that appear most.

Example 1:

W = {2, 6, 8, 2, 5, 6, 1, 10, 5}

Arrange the digits in order, (We have arranged them in Ascending order, you can also arrange them in Descending order)

W = {1, 2, 2, 5, 5, 6, 8, 10}

By counting the numbers, we can check which one is occurring the most. The above set has two modes 2 & 5 because both of these appear more than other numbers.

Example 2:

The head of the school told Mr. Dave to make a sheet of same-aged students in his class.

Data Collected:

12, 14, 11, 11, 12, 12, 15, 11, 10, 9, 8, 11, 12, 9, 8, 14

Let’s arrange the data in Ascending Order:

8, 8, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 14, 14, 15

Now, we can easily find the mode which is 11 and 12.

How to find a mode by grouping?

All the numbers in a set of digits have the same quantity of numbers. In this case, we find the mode by grouping the digits and checking which group shows more numbers than the others.

For example:

A = {36, 35, 1, 2, 3, 24, 23, 17, 13}

Arrange the digits in Ascending order,

A = {1, 2, 3, 13, 17, 23, 24, 35, 36}

All digits appear in the same quantity. So, we make a group of 5 to find the mode.

• 0 to 4: Three numbers (1, 2, and 3)
• 5 to 9: Zero numbers
• 10 to 14: Only one number (13)
• 15 to 19: Only one number (17)
• 20 to 24: Two numbers (23 and 24)
• 25 to 29: Zero number
• 30 to 34: Zero number
• 35 to 39: Two numbers (35)

In groups 0 to 4, maximum digits appear. So, we consider the middle digit “2” as its mode.

FAQ's

How to find the mode of a given set of numbers?

You can find a mode of a given set by counting the numbers. The number that appears for maximum times will be termed as the mode of that set.

Is it possible to have two modes for a single set?

Yes, it is possible to have two modes for a single set.

What is the “No Mode” condition?

When all elements or entries of a set occur only once, then the situation is called “No Mode” which means that it has not any mode quantity.

Can we get some answers for Mode and Mean?

It is possible to have the same results from Mode and Mean but it is not compulsory.