# Average Aptitude Concepts and Formulas

## Points to remember:

1) The average of n quantities of the same kind is equal to the sum of all the quantities divided by the number of quantities;

Average =

Sum of quantities = Average âˆ— Number of quantities

Number of quantities =

2) Average of two or more than two groups;

If the number of quantities in two groups are n_{1} and n_{2} respectively and their individual average is X and Y respectively, the combined average of the two groups is given by;

=

3) If the average of n_{1} quantities is X and the average of n_{2} quantities out of n_{1} quantities is Y, the average of the remaining quantities is given by;

=

4) The average of n quantities is equal to X. One quantity of value P is replaced with a new quantity having value Q the average of quantities becomes Y. Then Q is given by;

Q = P+n (Y-X)

5) The average of n quantities is equal to X. If we remove one quantity the average becomes Y, the value of the removed quantity is given by;

= n(X â€“ Y) + Y

And, if the average of n quantities is equal to X and on adding a new quantity the average becomes Y, the value of new quantity is given by;

= n ( Y â€“ X) + Y

### 6) Average of numbers:

**1) Natural numbers:**

- The average of first n consecutive natural numbers is given by; =
- The average of square of first n consecutive natural numbers is given by; =
- The average of cubes of first n consecutive natural numbers is given by; =

**2) Even numbers: **

- The average of first n consecutive even numbers is given by;

= n + 1 - Also, the average of first n consecutive even numbers starting from 2 to X, where the last even number is X, is given by;

= - The average of square of first n consecutive even numbers is given by;

= - Also, the average of square of first n consecutive even numbers starting from 2 to X, where the last even number is X, is given by;

=

**3) Odd numbers:**

- The average of first n consecutive odd numbers is equal to n.
- Also, the average of first n consecutive odd numbers starting from 1 to X, where the last odd number is X is given by;

= - The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by;

=

## Some quicker methods:

- The average of n numbers is X. If each number is multiplied by Y, the new average is given by;

= Initial average âˆ— Y - The average age of a group of boys is given. If the new average age after a boy joins the group is also given, the age of new boy is given by;

Age of new boy = New average + number of boys initially âˆ— increase in average - The average weight of a group of persons is given. If we replace a person in the group with another person and the new average is increased,

The weight of new person = weight of the removed person + no. of persons âˆ— increase in average. - The average of the marks obtained by students is given. The average of marks obtained by the passed students and failed students are also given, then
Number of passed candidates =

And, Number of failed students =

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