# Quick Review: Averages

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In this article, you will get an overview of the concept of averages and the related formulae.
Basic formula
Average = (Sum of Observations)/(No.of Observations)
###### Average Speed
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
###### Average in Terms of Age
• 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)
• 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)
###### Important Points:
• 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 n1 and n2 and their average is x and y respectively, then the combined average = .
• If the average of n1 quantities is x and the average of n2 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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