In this article, you are going to learn the basic concepts of average or arithmetic mean. Average is a very important area as far as the competitive exams are concerned. You will see questions based on arithmetic mean in almost all the competitive exams.

- Average is basically the Arithmetic mean of given items.

- Mathematically, Arithmetic Mean= average = Sum of terms/ No. of terms.

- When the difference between all the items is same (and the number of terms is odd), then the average is equal to the middle term. The average of the first and last term would also be the average of all the terms of the sequence.
- If x is added to all the items, then the average increases by x.
- If x is subtracted from all the items, then the average decreases by x.
- If every item is multiplied by x, then the average also gets multiplied by x.
- If every item is divided by x, then the average also gets divided by x.

From this example, you can learn that it is not necessary to apply the arithmetic mean formula in every question where you have to find the average, seeing the values of numbers, sometimes doing it logically would be of great help. This technique can reduce your time taken for a question by a huge margin. Needless to say time is the most important factor in a competitive paper.

Besides this, you can think logically that every officer is getting (300 - 150 = 150) Rs. 150 more than the average. Total of the extra money taken by all the officers together is 150 × 20 = 3000. Now every non-officer is getting (150 - 120) = Rs. 30 less than the average. How many officers will get Rs. 3000 less i.e. 3000/30 = 100. Hence there are 100 non-officers.

Must Read Average Articles

- Basics of Averages
- Average: Theory & Formulas
- Average/Arithmetic Mean: Concept explained with Examples

From this example, you can learn that it is not necessary to apply the mean formula in every case. Sometimes applying the extra item given/ taken can also help to find the average without much effort and calculations.

Suggested Action:

- This article tells us the approach to solve average problems in various forms. The techniques explained in this article, would make to solve the average questions in quick span of time and with much lesser effort and better accuracy. As the topic is very important, do remember to solve sufficient number of questions till you become an expert in the area.