**1. Common Formula used to calculate average**

__Ex. What is the average of 10, 11, 13, 15, 18, and 23?__Solution:

Sum of numbers= 10+11+13+15+18+23 = 90

Total numbers = 6

Average = 90/6 =15

**2. If the difference between the numbers is consonant or same, like 2,4,6,8 or 3, 6, 9, 12 then**

__Ex. Find the average of 4, 8, 12, 16, 20, and 24.____Solution:__

The difference between the numbers is consonant or same.

=14

3. Average of the first ‘n’ consecutive natural numbers is

3. Average of the first ‘n’ consecutive natural numbers is

__Ex. What is the average of the first 25consecutive natural numbers?__Solution:

=13

__2nd Method:__1,2,3,4,5,6,7,8,9,.....,20,21,22,23,24,25

Sum of numbers = 325, Total numbers = 25

=13

**4. Average of the first ‘n’ natural even number is**

__Ex. What is the average of the first 10 natural even numbers?__

__Solution:__=11

**5. Average of the first ‘n’natural odd numbers is**

Average = n

__Ex. What is the average of the first 8 natural odd numbers?__Solution:

Average = 8

__2nd Method:__1,3,5,7,9,11,13,15

Sum of numbers = 64, Total numbers = 8

=8

**6. Average of natural even numbers up to ‘n’**

__Ex. What is the average of the even numbers up to 22?__Solution:

Average = 12

__2nd Method:__2,4,6,8,10,12,14,16,18,20,22

Sum of numbers = 132, Total numbers= 11

=12

**7. Average of natural odd numbers up to ‘n’**

__Ex. What is the average of the odd numbers up to 17?__Solution:

Average = 9

__2nd Method:__1,3,5,7,9,11,13,15,17

Sum of numbers = 81, Total numbers= 9

=9

**8. Average of squares of first ‘n’ natural numbers**

__Ex. What is the average of the squares of the first 10 natural numbers?__Solution:

Average= 38.5

2nd Method:2nd Method:

1,4,9,16,25,36,49,64,81,100

Sum of numbers=385, Total number=10

Average= 38.5

Solution:

Average= 73.5

1,8,27,64,125,216

Sum of numbers=385, Total number=6

Average= 73.5

Solution:

Average= 17.5

5,10,15,20,25,30

Sum of numbers=105, Total numbers=6

Average= 17.5

**9. Average of the cubes of first ‘n’ natural numbers**__Ex. What is the average of the cubes of the first 6 natural numbers?__Solution:

Average= 73.5

__2nd Method:__1,8,27,64,125,216

Sum of numbers=385, Total number=6

Average= 73.5

10. Average of ‘n’ multiple of ‘a’10. Average of ‘n’ multiple of ‘a’

__Ex. What is the average of 6 multiple of 5?__Solution:

Average= 17.5

__2nd Method:__5,10,15,20,25,30

Sum of numbers=105, Total numbers=6

Average= 17.5

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