![](https://4.bp.blogspot.com/-zLXYcw4ipTk/WTUuuElsDhI/AAAAAAAAKhs/8Gv-Uptp1I0F2RbjXRSR9VQ0N7Mgrtu9ACK4B/s400-rw/Average%2BFormulas.png)
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
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
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’
![](https://3.bp.blogspot.com/-N09-l3-yOoE/WTUSbXL6GWI/AAAAAAAAKgA/nuDoGwD6CZE__dR24LZEze0PwklUCfbagCLcB/s1600-rw/10.PNG)
Ex. What is the average of the even numbers up to 22?
Solution:
![](https://3.bp.blogspot.com/-d0YUmY-kUi0/WTUSbdMJxzI/AAAAAAAAKgE/1WXiIkH_Rwc5o9oMvCRVSaDDNts1qsaPgCLcB/s1600-rw/11.PNG)
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
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
![](https://2.bp.blogspot.com/-svp_hu5dEj8/WTUSdAJ2LlI/AAAAAAAAKgY/gZYvANQoUjo8G2jnXxIQTIXE7TBiO82EACLcB/s1600-rw/16.PNG)
Ex. What is the average of the squares of the first 10 natural numbers?
Solution:
![](https://3.bp.blogspot.com/-jP4GuTkV6GI/WTUSdV4RpoI/AAAAAAAAKgc/ulrpY233QH4wiOJgkEsG9xQVYhdheG8PACLcB/s1600-rw/17.PNG)
Average= 38.5
2nd Method:
1,4,9,16,25,36,49,64,81,100
Sum of numbers=385, Total number=10
Ex. What is the average of the squares of the first 10 natural numbers?
Solution:
Average= 38.5
2nd Method:
1,4,9,16,25,36,49,64,81,100
Sum of numbers=385, Total number=10
Average= 38.5
9. Average of the cubes of first ‘n’ natural numbers
![](https://3.bp.blogspot.com/-tEzcZrdskEU/WTUSd4g1DPI/AAAAAAAAKgk/M4k7riAewU0di_GntfJavJN_LRJ57Xl3wCLcB/s1600-rw/19.PNG)
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’
![](https://4.bp.blogspot.com/-t2CPGHnU58U/WTUSg5exN6I/AAAAAAAAKhQ/V9idyqiHABMnVLEleEHsPhXb79Dbuh2xACLcB/s1600-rw/22.PNG)
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
![](https://4.bp.blogspot.com/-tTLxH3WRKLc/WTUShRBishI/AAAAAAAAKhY/IwYGfKjqjt8NvOtg38Y3Ex9ZkGy2k8BuACLcB/s1600-rw/24.PNG)
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’
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