Important Quantitative Fromulae for Aptitude tests – Average

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1. Average = Sum of quantities/ Number of quantities

2. Sum of quantities = Average  Number of quantities

3. The average of first n natural numbers is (n +1)/2

4. The average of the squares of first n natural numbers is (n +1)(2n+1)/6

5. The average of cubes of first n natural numbers is n(n +1)2 /4

6. The average of first n odd numbers is given by (last odd number +1)/2

7. The average of first n even numbers is given by (last even number + 2)/2

8. The average of first n consecutive odd numbers is n

9. The average of squares of first n consecutive even numbers is 2(n+1)(2n+1)/3

10.The average of squares of consecutive even numbers till n is (n+1)(n+2)/3

11.The average of squares of squares of consecutive odd numbers till n is n(n+2)/ 3.

12. If the average of n consecutive numbers is m, then the difference between the smallest and the largest number is 2(m-1)

13. If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, the combined average is (n1x +n2y)/( n1 + n2)

14. The average of n quantities is equal to x. When a quantity is removed, the average becomes y. The value of the removed quantity is n(x-y) + y

15. The average of n quantities is equal to x. When a quantity is added, the average becomes y. The value of the new quantity is n(y-x) + y