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Average Tips and Tricks for Government Exams

Introduction

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 formula that is sum of observations divide by Number of observations.
Average = Sum of Quantities/Number of quantities ⇒ S = A × N
Average Tips and Tricks for Government Exams

Theory

Averages can be defined as the central value in a set of data. Average can be calculated simply by dividing the sum of all values in a set by the total number of values. In other words, an average value represents the middle value of a data set. The data set can be of anything like age, money, runs, etc.
Average = [ Sum of Data (or observations) in a set / Number of data (or observations) in that set]

Tips 

  • If all the numbers are increased by 'a’, then their average will also be increased by 'a’.
  • If all the numbers are decreased by ‘a’, then their average will also be decreased by 'a’.
  • If all the numbers are multiplied by 'a’, then their average will also be multiplied by 'a'.
  • If all the numbers are divided by 'a', then their average will also be divided by 'a’.

Formula

  • Average = Sum of quantities/ Number of quantities
  • Sum of quantities = Average * Number of quantities
  • The average of first n natural numbers is (n +1) / 2
  • The average of the squares of first n natural numbers is (n +1)(2n+1) / 6
  • The average of cubes of first n natural numbers is n(n+1)2 / 4
  • The average of first n odd numbers is given by (last odd number +1) / 2
  • The average of first n even numbers is given by (last even number + 2) / 2
  • The average of squares of first n consecutive even numbers is 2(n+1)(2n+1) / 3
  • The average of squares of consecutive even numbers till n is (n+1)(n+2) / 3
  • The average of squares of squares of consecutive odd numbers till n is n(n+2) / 3
  • If the average of n consecutive numbers is m, then the difference between the smallest and the largest number is 2(m-1)
  • If the number of quantities in two groups be n1 and n2 and their average is x and y respectively, the combined average is (n1x + n2y) / (n+  n2)
  • The average of n quantities is equal to x. When a quantity is removed, the average becomes y. The value of the removed quantity is n(x-y) + y
  • The average of n quantities is equal to x. When a quantity is added, the average becomes y. The value of the new quantity is n(y-x) + y

Solved Examples

Question for Tips & Tricks: Average
Try yourself:The average mark in 2 subjects is 35 and in three other subject is 40.Then find the average mark in all the five matches ?
View Solution

Question for Tips & Tricks: Average
Try yourself:The average age of Husband and wife was 30yr, 4 yr ago. What will be their average age at present ?
View Solution

Question for Tips & Tricks: Average
Try yourself:The average of 5 consecutive number is 58.Find the first number ?
View Solution

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FAQs on Average Tips and Tricks for Government Exams

1. What is the definition of average?
Ans. Average is a mathematical term that represents the central tendency of a set of numbers. It is calculated by adding all the numbers in the set and then dividing the sum by the total count of numbers.
2. How is the average calculated?
Ans. To calculate the average of a set of numbers, you need to add all the numbers together and then divide the sum by the total count of numbers. For example, if you have the numbers 5, 10, and 15, you would add them together (5+10+15 = 30) and then divide by the count of numbers (3). So, the average would be 30/3 = 10.
3. What is the importance of average in statistics?
Ans. Average is an important statistical measure as it provides a summary of the data set. It helps in understanding the central tendency and overall value of the data. It is commonly used in various fields such as economics, finance, and social sciences to analyze and interpret data.
4. Can the average be misleading?
Ans. Yes, the average can sometimes be misleading. It is a single value that represents the central tendency of the data, but it may not accurately reflect the distribution or the outliers in the data set. For example, if you have a data set with extreme values, the average may be significantly affected by these outliers and may not represent the typical value.
5. How can the average be used to compare data sets?
Ans. The average can be used to compare data sets by calculating the average of each set and comparing the results. By comparing the averages, you can get an idea of which set has a higher or lower central tendency. However, it is important to consider other statistical measures and factors to gain a comprehensive understanding of the data and make meaningful comparisons.
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