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Important Formulas - Average - Tricks & Shortcuts

1) Average:

Average = (Sum of observations/Number of observations) 

Example:
If a teacher tutored five students and they subsequently scored 96, 94, 92, 87, and 81, what was the average score of the students whom the teacher tutored?
N = 5 since there are 5 students(Number of Observations)
S = 96 + 94 + 92 + 87 + 81 = 450(Sum of Observations)

Average = S/N = 450/5 = 90

2) Average Speed:

Suppose a man covers a certain distance at x kmph and an equal distance at y kmph.

Then, the average speed druing the whole journey is [(2xy)/(x + y)] kmph.

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

4) Average of first n natural  EVEN numbers is = (n+1)

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

6) Average of first n natural  odd numbers is = n
             
7) Average of natural odd numbers up to n is = (n+1)/2
               
8) Average of n multiples of p will be = {p(n+1)}/2

9) 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)

10) 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)

11) 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

12) 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



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