What is Mean?

Mean is the most commonly used measure of central tendency. It actually represents the average of the given collection of data. It is applicable for both continuous and discrete data.

It is equal to the sum of all the values in the collection of data divided by the total number of values.

Suppose we have n values in a set of data namely as 

then the mean of data is given by:

For grouped data, we can calculate the mean using three different methods of formula.

What is Median?

Generally median represents the mid-value of the given set of data when arranged in a particular order.

Median: Given that the data collection is arranged in ascending or descending order, the following method is applied:

• If number of values or observations in the given data is odd, then the median is given by

observation.

If in the given data set, the number of values or observations is even then the median is given by the average of 

Median for grouped data can be calculated using the formula,

What is Mode?

The most frequent number occurring in the data set is known as the mode.

Consider the following data set which represents the marks obtained by different students in a subject.

Name	Anmol	Kushagra	Garima	Ashwini	Geetika	Shakshi
Marks Obtained (out of 100)	73	80	73	70	73	65

The maximum frequency observation is 73 ( as three students scored 73 marks), so the mode of the given data collection is 73.

We can calculate the mode for grouped data using the below formula:

Example: The given table shows the scores obtained by different players in a match. What is mean and median of the given data?

S.No	Name	Runs Scored
1	Sachin	80
2	Yuvraj	52
3	Virat	40
4	Sehwag	52
5	Rohit	70
6	Harbhajan	1
7	Dhoni	6

Solution:

i)  The mean is given by 

The mean of the given data is 43.

ii) To find out the median let us first arrange the given data in ascending order

Name	Harbhajan	Dhoni	Virat	Yuvraj	Sehwag	Rohit	Sachin
Runs	1	6	40	52	52	70	80

As the number of items in the data is odd. Hence, the median is