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May 30, 2015

AVERAGE SHORTCUT FORMULAS

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Important Formulas related to AVERAGE




Average Formulas
Average: An average or can say arithmetic mean of n number observations is, total sum of n observations divided by n.

   Average = Sum of observations/Number of observations




Average Speed:
v  If a person covers the same distance at two different speeds i.e x km/h and y km/h respectively, Then his total Average Speed = (2xy)/(x+y)

v  If a person covers the same distance at different speeds x km/h, y km/h and z km/h  respectively, Then his total Average Speed  =(3xyz)/(xy+yz+zx)

·         If the average of  n1 observations is x1 and average of n2 observations is x2, then the Average of total observations(n1+n2)  =(n1x1+n2x2)/(n1+n2)

·         Suppose if the total average age of x members of a family is y years and Now if  a new member joins the family and the new average age the family is n, then the age of new member will be  =[n-x(n-y)] years

·         Total average age of x members of a family is y years Now if  a member leaves the family, and the new average age of the family is n, then the age of that member will be =[n+x(y-n)] years

·         Average of first n consecutive natural numbers =(n+1)/2

·         Average of first n natural  Even numbers =(n+1)

·         Average of natural even numbers up to n =(n/2)+1

·         Average of first n natural odd numbers=n

·         Average of natural odd numbers up to n =(n+1)/2

Some Important Points to be remember:

ü  If the value of each observation is increased by the same value n, then their total average will also be increase by n.

ü  If the value of each observation is decreased by the same value n, then their total average will also be decrease by n.

ü  If the value of each observations is multiplied by the same value n, then their total average will also be get multiplied by n.

ü  If the value of each observation is divided by the same value n, then their total average will also be get divided by n.


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