 # Difference Between Mean and Median

In Mathematics, the most important two terms are mean and median. So. it is necessary to learn the difference between Mean and Median. To understand the difference between the two, you have to be aware of the definitions of both the terms. In this article, we are going to have a look at the definition, mean median formula and the difference between mean and median along with examples here.

## What is Mean?

Mathematical mean can simply be defined as the list of numbers that are used to describe a central tendency. The method to calculate mean is simple enough, the variables need to be added and divided by the number of items in the overall sample. Consider a sample value, say x1, x2, … , xn

So, the formula for calculating the mean is given as:

Mean =  (x1, x2, … , xn)/n

Where “n” is the total number of items in the sample.

## What is the Median?

Median on the other hand can simply be defined as the number that is found in the middle of the set. Median is an essential quantity that can be used for separating the available sample into two; the higher half sample, as well as the lower half sample, can be procured in this method. To proceed with the process of finding the median of the given data, first, arrange the given set of numbers on the ascending order, and then find the middle value from the centre of the distribution. This condition is suitable if we have an odd number of observations. But, in case of even number of observation, there is no single median value. So, in this case, add the two numbers in the middle and then divide it by 2. The obtained value is taken as a median value.

## Key Difference between Mean and Median

Here, the major difference between mean and median is listed below. Go through the following differences.

Difference between Mean and Median
Mean Median
The average arithmetic of a set of numbers is called Mean. The method of separating the higher sample with the lower value, usually from a probability distribution is termed as the median
The application for the mean is for normal distributions The primary application for the median is skewed distributions.
There are a lot of external factors that limit the use of Mean. It is much more robust and reliable for measuring the data for uneven data.
Mean can simply be calculated by adding all the values and dividing the total by the number of values. Median can simply be calculated by listing all the numbers available in the set in arranging the order and then finding the number in the centre of the distribution.
Mean is considered as an arithmetic average. Median is considered as a positional average.
It is sensitive to outliers It is not sensitive to outliers.
It represents the centre of gravity of the data set. It represents the centre of gravity of the midpoint of the data set.

Thus, these are the major differences between Mean and Median. It is essential to know the major differences between the two.

### Mean and median Problem

Question:

Find the mean and median for the following data:

3, 5, 4, 1, 8, 6, 9

Solution:

Given Data: 3, 5, 4, 1, 8, 6, 9

No. of. data = 7

The mean for the following data is given as:

Mean =  (3 +5 + 4 + 1 + 8 + 6 + 9)/7

Mean = 36/7 = 5. 14

Therefore, the mean of the following data is 5. 14

To find median:

Step 1: Arrange the given set of data in ascending order

So, it becomes: 1, 3, 4, 5, 6, 8, 9

Step 2: Since the number of data is odd, take the middle value

So, the middle value of the given data is 5.

Thus, the median value is 5.