Mean vs Median in Math? Know the Difference with Examples - BYJUS

# Difference Between Mean and Median

In statistics, measures of center are commonly used to determine various characteristics of a data set. There are three measures of center, namely, mean, median, and mode. Mean, median, and mode have different applications and uses. In this article, we will try and learn the difference between the mean and the median of a data set.     ...Read MoreRead Less

## Mean

Mean can be defined as the average of a data set. We can also say that it is the sum of all elements in a data set divided by the total number of elements in a data set. The most common type of mean is the arithmetic mean.

Arithmetic mean $$(\bar{x})~=~\frac{\text{Sum of all elements in a data set}}{\text{Total number of elements in a data set}}$$

$$(\bar{x})$$: It is used to denote the arithmetic mean.

For example, let us consider a sample set having n number of entities in the data set, that are: $$x_1,~x_2~,x_3,….~,x_n$$

Then the arithmetic mean, or simply mean, can be calculated by using the formula:

$$\bar{x}~=~\frac{x_1~+~x_2~+~x_3~+…..~+~x_n}{n}$$

where $$n$$ represents the number of items in the data set.

## Median

The median, on the other hand, is simply the number or value that lies in the middle of a data set.

The median can be calculated by arranging the data set in a specific order. They can be arranged in ascending or descending order. This is how you find the median for even and odd data sets:

• If the number of elements in a data set is even, the median can be calculated by taking the mean of the two middle numbers.

For example: If $$x_1,~x_2,~x_3,~x_4,~x_5,$$  and $$x_6$$ are arranged in ascending order, then:

Median $$=~\frac{x_3~+~x_4}{2}$$

• If the number of elements in a data set is odd, the median is the middle of the number in the data set.

For example: If $$x_1,~x_2,~x_3,~x_4,~x_5$$ are arranged in ascending order then:

Median $$=~x_3$$

## What is the difference between Mean and Median?

S.No

Mean

Median

1

The arithmetic average of all the elements of a data set is known as the mean.

The middle value of a data set when all the elements are arranged in order is known as the median. It is also used to separate the higher values from the lower values.

2

It is recommended not to use the mean for skewed data.

It is recommended to use the median for skewed data.

3

Mean is a type of arithmetic average.

Median is a type of positional average.

4

Mean is highly sensitive to outlier data.

Median is not very sensitive to outlier data.

5

The use of the mean can be limited due to external factors and errors caused by it.

Median is not very sensitive to outlier data.

## Solved Examples

Example 1: Find the median for the following data set:

2, 1, 8, 3, 9, 10.

Solution:

Given data: 2, 1, 8, 3, 9, 10

1, 2, 3, 8, 9, 10                           Arrange the data in ascending order.

Number of elements = 6 (Even)

Median $$=~\frac{\text{Sum of middle data}}{2}$$

$$=~\frac{3~+~8}{2}$$                         Substitute

$$=~5.5$$                           Simplify

So, the median of the data is 11.5.

Example 2: Find the median for the following data set:

3, 11, 9, 5, 8.

Solution:

Given data 3, 11, 9, 5, 8

3, 5, 8, 9, 11                            Order the data.

Number of elements = 5 (Odd)

Median = 8

So, the median of the data is 8.

Example 3. Find the mean of the following data sets:

2, 4, 3, 7, 1.

Solution:

Given data 2, 4, 3, 7, 1

Number of elements = 5

Mean $$=~\frac{\text{Sum of data}}{\text{Total number of data elements}}$$

$$=~\frac{2~+~4~+~3~+~7~+~1}{5}$$             Substitute

$$=~\frac{17}{5}$$

$$=~3.4$$                               Simplify

So, the mean of the data is 3.4.

Example 4. Find the mean of the following data sets:

10, 0, 50, 30, 20.

Solution:

Given data 10, 0, 50, 30, 20

Number of elements = 5

Mean $$=~\frac{\text{Sum of data}}{\text{Total number of data elements}}$$

$$=~\frac{10~+~0~+~50~+~30~+~20}{5}$$               Substitute

$$=~\frac{110}{5}$$

$$=~22$$                                      Simplify

So, the mean of the data is 22.