Quick Review: Averages

Average Speed

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
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• 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