How to find Mean, Median, Mode and Range ?

Finding Mean, Median, Mode and Range 


This post helps you to understand few very important and most commonly asked Statistics terms like Mean, Median, Mode and Range. After reading this complete post you are able to solve any questions based on these terms. Previously we have all ready posted Statistics notes in PDF . 

These terms are explained in crystal clear manner with illustrative examples. If you still have any problem please comment below.
mean-median-mode-range

MEAN, MEDIAN, MODE AND RANGE


MEAN


Mean – Mean is average of a group of numbers.
To find the mean add all the numbers together then divide that sum by the amount of numbers.
Another name for mean is average.

Key Point- “Mean is find by evening out the numbers

Example:
Q. Find Mean of 3,6,3,2,6
Ans-  Mean= (3+6+3+2+6)/5 = 4

Illustrative Example:


Q. Find Mean of 9,11,13,19,23,27
Ans-  Mean= (9+11+13+19+23+27)/6 = 17

Q. Find Mean of 3,10,15,28
Ans-  Mean= (3+10+15+28)/4 = 14

Q. Find Mean of 2,3,8,12,20
Ans-  Mean= (2+3+8+12+20)/5 = 9

Q. Find Mean of 27,34,42,53
Ans-  Mean= (27+34+42+53)/4 = 39


MEDIAN


Median – The middle number in a set of ordered numbers is called median.
To find the median list all the numbers in correct order, being sure to include any doubles. Then find the middle number.
If there is an odd amount of numbers - the median is the middle number.
If there is an even amount of numbers - the median is found by adding the middle two numbers together and dividing the sum by 2 . The resulting number is the median.

Steps:
Step-1. - Arrange the given set of number in an order of least to greatest.
Step-2. - If there is an odd amount of numbers - the median is the middle number.
Step-3. - If there are two middle numbers, find the mean of these two numbers.

Key Point- “Median is in the Middle

Example:
Q. Find median of given set of numbers- 2,4,8,11,14
Solution:
First arrange in an order of least to greatest – 2,4,8,11,14
Now find middle of this set- 8
So median = 8 (Ans)

Q. Find median of given set of numbers- 22,19,25,20,28
Solution:
First arrange in an order of least to greatest – 19,20,22,25,28
Now find middle of this set- 22
So median = 22 (Ans)

Q. Find median of given set of numbers- 19,20,22,26,28,29
Solution:
First arrange in an order of least to greatest – 19,20,22,26,28,29
Now find middle of this set- 22 and 26
Here two number in middle So median= (22+26)/2= 48/2= 24
So median = 24 (Ans)

Q. Find median of given set of numbers- 17,11,8
Solution:
First arrange in an order of least to greatest – 8,11,17
Now find middle of this set- 11
So median = 11 (Ans)

Q. Find median of given set of numbers- 30,9,5,12,20
Solution:
First arrange in an order of least to greatest –5,9,12,20,30
Now find middle of this set- 12
So median = 12 (Ans)

Q. Find median of given set of numbers- 32,8,3,13,15,20
Solution:
First arrange in an order of least to greatest – 3,8,13,15,20,32
Now find middle of this set- 13 and 15
Here two number in middle So median= (13+15)/2= 28/2= 14
So median = 14 (Ans)

Q. Find median of given set of numbers- 54,6,82,68,26,79
Solution:
First arrange in an order of least to greatest – 6,26,54,68,79,82
Now find middle of this set- 54 and 68
Here two number in middle So median= (54+68)/2= 112/2= 61
So median = 61 (Ans)


MODE


Mode - The mode is that number which appears the most frequently in a set of given numbers.
There can be more than one mode provided they are listed the same amount of times.

Steps:
Step 1 – Arrange the numbers in order of least to greatest.
Step 2 – Find the number that is repeated the most.

Key Point- “Mode is the Most Popular”

Example:

Q. Find Mode of given set of numbers – 2,2,4,8,11,14
Solution:
First arrange these numbers in an order of least to greatest – 2,2,4,8,11,14
Now find number that is repeated the most- 2
So, Mode= 2 (Ans)

Q. Find Mode of given set of numbers – 22,19,25,20,19
Solution:
First arrange these numbers in an order of least to greatest – 19,19,20,22,25
Now find number that is repeated the most- 19
So, Mode= 19 (Ans)

Q. Find Mode of given set of numbers – 30,9,5,9,20
Solution:
First arrange these numbers in an order of least to greatest – 5,9,9,20,30
Now find number that is repeated the most- 9
So, Mode= 9 (Ans)

Q. Find Mode of given set of numbers – 2,3,3,10,10,5,10,11
Solution:
First arrange these numbers in an order of least to greatest – 2,3,3,5,10,10,10,11
Now find number that is repeated the most- 10
So, Mode= 10 (Ans)

Q. Find Mode of given set of numbers – 23,23,28,32,22,33
Solution:
First arrange these numbers in an order of least to greatest – 22,22,23,28,32,33
Now find number that is repeated the most- 22
So, Mode= 22 (Ans)


RANGE


Range - is the difference between the greatest and the least value in a set of numbers.
It is found by subtracting the lowest from the highest.

Steps:
Step 1 – Arrange the numbers in order from least to greatest.
Step 2 – Find the lowest and highest numbers.
Step 3 – Find the difference between these 2 numbers.

Key Point- “ Range is the distance between the lowest and highest number.”

Example:

Q. What is the Range?
2,2,4,8,11,14
Solution:
First arrange these numbers in an order of least to greatest – 2,2,4,8,11,14
Now find the lowest and the highest numbers – 2 and 14
So, Range= 14-2 = 12 (Ans)

Q. What is the Range?
22,19,25,20,28
Solution:
First arrange these numbers in an order of least to greatest – 19,20,22,25,28
Now find the lowest and the highest numbers – 19 and 28
So, Range= 28-19 = 9 (Ans)

Q. What is the Range?
30,9,5,9,20
Solution:
First arrange these numbers in an order of least to greatest – 5,9,9,20.30
Now find the lowest and the highest numbers – 5 and 30
So, Range= 30-5 = 25 (Ans)

Q. What is the Range?
23,22,28,32,22,33
Solution:
First arrange these numbers in an order of least to greatest – 22,22,23,28,32,33
Now find the lowest and the highest numbers – 22 and 33
So, Range= 33-22 = 11 (Ans)

Q. What is the Range?
32,9,4,12,20
Solution:
First arrange these numbers in an order of least to greatest – 4,9,12,20,32
Now find the lowest and the highest numbers – 4 and 32
So, Range= 32-4 = 28 (Ans)



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