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# Quantitative Aptitude :: Average

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## Average Important Formulas

The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average. The main term of average is equal sharing of a value among all, where it may share persons or things. We obtain the average of a number using the formula that is the sum of observations divides by Number of observations.

1. Average:

Formula to find Average = $$\frac{Sum of observations}{Number of observations}$$

2. Average Speed Formula:

What is the formula for average speed? Suppose a man covers a certain distance at x kmph and an equal distance at y kmph.

Then, the average speed during the whole journey will be $$\left(\frac{2xy}{x+y}\right)$$kmph.

Average Methods shortcut tricks

• If both the time taken are equal i.e t1 = t2 = t,then, $$\frac{t1 + t2}{2}$$

• The average of odd numbers from1 to n is = $$\frac{[Last \ odd \ no. + 1]}{2}$$.

• The average of even numbers from1 to n is = $$\frac{[Last \ even \ no. + 2]}{2}$$.

• The Average of any number of quantities is sum of their quantities by the number of quantities (n) => Average = $$\frac{Sum of quantities}{n}$$.

• If there are two types of items say A and B , A has m number of sub items and B has n number of sum items then the average of A and B is $$\frac{A \times m + B \times n}{m+n}$$.

• If a vehicle travels from one place to another at a speed of a kmph but returns at the speed of b kmph then its average speed during the whole journey is $$\left(\frac{2ab}{a + b}\right)$$ kmph.

• Out of three numbers, first number is x times of the second number and y times of the third number. If the average of all the three numbers is z then the first number is $$\frac{3xyz}{xy + x + y}$$

• The average age of a group of N student is 'X' years. If M students joins, the average age of the group increases by 'Y' years, then the average age of the new students = $$x + \left(1 + \frac{N}{M}\right)\times Y$$ years.

• The average age of a group of N student is 'X' years. If M students joins, the average age of the group decreased by 'Y' years, then the average age of the new students = $$x - \left(1 + \frac{N}{M}\right)\times Y$$ years.

• The average age of a group of N student is 'X' years. If M student (Rahul) join the group, the average age of the group increases by 'Y' years, then the age of the new student (Rahul) is = $$x + \left(1 - \frac{N}{M}\right)\times Y$$ years.

• The average age of a group of N student is 'X' years. If M student (Ram) left the group, the average age of the group decreased by 'Y' years, then the age of the new student (Ram) was = $$x - \left(1 - \frac{N}{M}\right)\times Y$$ years.

• In a group of N persons whose average age is increased by 'Y' years when a person of 'X' years is replaced by a new man. Then the age of new comer is = $$\left(X + N \times Y\right)$$ years.