Average shortcut formulas-All types of average formulas

Here are some of the Average shortcut formulas which will help you solve Average problems quickly and easily.
What is Average of Numbers?

The average of a number of items of the same type is their sum divided by the number of those items.
Average of consecutive first n natural numbers is
                 =(n+1)/2
Average of first n natural  EVEN numbers is
                =(n+1)
Average of natural even numbers up to n is
                =(n/2)+1
Average of first n natural  odd numbers is
                =n
Average of natural odd numbers up to n is
                 =(n+1)/2
Average of n multiples of p will be
                 ={p(n+1)}/2
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If a person covered a certain distance at a speed of x km/h and y km/h respectively, then his average speed will be
                = (2xy)/(x+y)
If a person covers a certain distance at a speed of x km/h and y km/h and z km/h respectively, then his average speed will be
                =(3xyz)/(xy+yz+zx)
If the average of  n1 items is p1 and average of n2 items is p2 then the average of total items (n1+n2) will be 
                =(n1p1+n2p2)/(n1+n2)
The average of ages of x members of a family is y years.   Now if  a new member joins the family, then the new average of ages of all the members is z. then the age of new member will be
                =[z-x(z-y)] years

The average of ages of x members of a family is y years.   Now if  a member leaves  the family, then the new average of ages of all the members is z. then the age of that member will be
                =[z+x(y-z)] years