In this article, you will get an overview of the concept of averages and the related formulae.

Average = (Sum of Observations)/(No.of Observations)

If a person travels a certain distance at the speed of x km/hr and the same distance at y km/hr, then the average speed of the whole distance can be calculated by = 2xy/(x+y)

If a person covers P kms at x km/hr, Q kms at y km/hr and R kms at z km/hr, then the average speed in covering the whole distance can be calculate by

- When a person replaces another person then:
- If the average is increased, then

Age of new person= Age of person who left + (Increase in average * total number of persons) - If the average is decreased, then

Age of new person= Age of person who left - (Decrease in average * total number of persons)

- If the average is increased, then
- When a person joins the group:
- In case of an increase in average,

Age of new member= Previous average + (Increase in average * Number of members including new member) - In case of decrease in average,

Age of new member= Previous average - (Decrease in average * Number of members including new member)

- In case of an increase in average,

- In case of odd number of terms with same difference, the average will be the middle term.
- In case of even number of terms with same difference, the average will be the average of two middle terms.
- If the number of quantities in two groups be n
^{1}and n^{2}and their average is x and y respectively, then the combined average = . - If the average of n
^{1}quantities is x and the average of n^{2}quantities out of them is y, the average of the remaining group = - The average of first n natural numbers = (n+1)/2
- The average of squares of first n natural numbers = (n+1)(2n+1)/6
- The average of cubes of first n natural numbers = n(n+1)
^{2}/4 - The average of odd numbers from 1 to n = (last odd number+1)/2
- The average of even numbers from 1 to n = (last even number+2)/2
- The average of squares of first n odd numbers = (2n+1)(2n-1)/3
- The average of first n odd numbers = n

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