# Average

Average is the most important topic that has been an integral part of syllabus of most of the competitive exams like SSC, CAT, GATE, Railways and many more. Every year there is question from this part of syllabus so we should practice it as much as we can. So lets start learning basic concepts. Average and mean are both same and been used in place of each other so don’t get confused.

Average refers to the sum of numbers divided by n or can be said that the sum of the numbers divided by how many numbers are being averaged.

Average = (Sum of Observations/Number of Observations)

One of the most general question that comes in many competitive exam is to find the average speed of a man given that he travels a certain distance with x kmph and an equal distance at y kmph.

This problem can be solved by following formula :-

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 is (2xy/(x+y)) kmph.

Lets solve some questions on this topic.

Example :- Get the average of first 40 natural numbers.

Solution :- First of all we should know the sum of first 40 natural numbers it can be calculated by following formula

Sum of first n natural numbers = n(n+1)/2

So, sum of first 40 natural numbers = (40 x 41 )/2 = 820

Average = 820/40 = 20.5

Example :- Find the mean of first 20 multiples of 7.

Solution :- Average = (sum of observations /total number of observations)

= 7(1+2+3+4+……..+20)/(20)= (7x20x21/20×2)= (147/2) = 73.5

Example :- Calculate the mean of all prime number between 30 and 50.

Solution :- Prime numbers between 30 and 50 are 31,37,41,43,47

= (31+37+41+43+47)/5 = 199/5 = 39.8

Reference Book :- Quantitative Aptitude by R.S. Aggarwal

Test how much you have learnt Here..!!