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**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.

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__MEAN, MEDIAN, MODE AND RANGE__

__MEAN, MEDIAN, MODE AND RANGE__

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__MEAN__

__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**

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__MEDIAN__

__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- “Me*__d__ian

*is in the*

*Mi*__dd__le

*”***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)

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__MODE__

__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)

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__RANGE__

__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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