Average Aptitude Concepts
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 ∗ 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 (YX)
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 – 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 – 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 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 first n consecutive even numbers is given by;

 The average of square of first n consecutive even numbers 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 ∗ 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 ∗ 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 ∗ 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, thenNumber of passed candidates =
And, Number of failed students =
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