## 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; 2) Average of two or more than two groups; 3) If the average of n 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; 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; ## 6) Average of 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; =
- 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;
=
- 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, then
Number of passed candidates = And, Number of failed students =
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