Averages Formulas

Concept of Average:
Assume 5 friends went to a movie.  If the total money with the friends is equal to 1000 then we say that average money with each person is Rs.200/-  But it is not necessary that each person has Rs.200.
Some may have more money than the others, but the total money is equal to Rs.1000.
Let us say Person E is rich and he bought Rs.500 to the movie.  So the money with the remaining friends is equal to Rs.500.  If E has not come to the movie, the average money with the other friends comes down to $\dfrac{{500}}{4}$ = Rs.125.  If E has bought Rs.125 to the movie the average stands at Rs.125.  But he has Rs.375 more than the average required.  And this extra amount is distributed among all the friends equally, so that each person gets $\dfrac{{375}}{5} = 75$ extra. That is why final average = 125  +  75 = Rs.200.

Formula 1:
Average or mean: The Mean (Average) of a group of numbers is the sum of the numbers divided by the number of numbers:
Average or Mean = Sum of the observations / Number of observations

Formula 2:
If the average of ‘m ’ quantities is ‘x ‘ and the average age of ‘ n ‘ other quantities is ‘y ‘ then the average of all of them put together is = $\displaystyle\frac{{mx + ny}}{{m + n}}$

Formula 3:
If the average age of ‘m ‘ quantities is ‘x ‘ and the average age of ‘n ’ quantities out of them (m quantities) is ‘ y ‘ then the average of the rest of the quantities is = .$\displaystyle\frac{{mx - ny}}{{m - n}}$

Formula 4:
If the average of ‘ n ‘ numbers is ‘ x ’ and if ‘ k ‘ is added to or subtracted from each given number the average of ‘ n ‘ numbers becomes (x+k) or (x-k) respectively. In the other words average value will be increased or decreased by ‘ k ‘.

Formula 5:
If the average of ‘ n ‘  numbers is ‘ x ‘ and if each given number is multiplied to or divided by ‘ k ‘ then the average of n numbers becomes kx or $\displaystyle\frac{x}{k}$ respectively.

Formula 6:
If a person travels a distance at a speed of x km/hr and the same distance at a speed of y km/hr then the average speed during the whole journey is given by $\displaystyle\frac{{2xy}}{{x + y}}$ km/hr.
If a person covers A km at x km/hr and B km at y km/hr and C km at z km/hr, then the average speed in covering the whole distance is $\displaystyle\frac{{A + B + C}}{{\displaystyle\frac{A}{x} + \frac{B}{y} + \frac{C}{z}}}$km/hr.

Formula 7:
The average of n (where n is an odd number) consecutive numbers is always the middle number E.g. 1, 3, 5, 7, 9.
 The Average = Middle number = 5

Formula 8:
The average ‘ n ‘ (where n is even number) consectuive numbers is the average of the two middle numbers.
E.g. Average of (2, 4, 6, 8, 10, 12) = $\displaystyle\frac{{6 + 8}}{2}$ = 7