# 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.

**Table of Contents**

## 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.