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
Solution:
The difference between the numbers is consonant or same.
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:
Average= 10+1 =11
2nd Method:
2,4,6,8,10,12,14,16,18,20
Sum of numbers= 110, Total numbers= 10
2nd Method:
2,4,6,8,10,12,14,16,18,20
Sum of numbers= 110, Total numbers= 10
=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’
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
1,3,5,7,9,11,13,15
Sum of numbers = 64, Total numbers = 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
7. Average of natural odd numbers up to ‘n’
Ex. What is the average of the odd numbers up to 17?
Solution:
2nd Method:
1,3,5,7,9,11,13,15,17
Sum of numbers = 81, Total numbers= 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:
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
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
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:
2nd Method:
1,8,27,64,125,216
Sum of numbers=385, Total number=6
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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