Average Concepts

Understanding the Concepts of Average

You can now understand the fundamental concepts of Average. Listed below are the different Average concepts:

1. What is Average?
2. How to find the Average for given numbers?
3. Rules of Average
4. Average of two or more groups taken together
5. What is Average Speed?

1. What is Average?

In mathematics, Average is defined as the mean value, which is equal to the ratio of the sum of all values in a set to the total number of values/units present in the set.

The data can be anything like age, money, runs, etc. Average has many applications in real-life.

Average = sum of elements / number of elements

Example Problem

The Average of 3, 6, and 9 is 3 + 6 + 9 = 18÷ 3 = 6. So the Average is 6. It means 6 is the central value of 3, 6, and 9.

Therefore, Average means to find out the mean value of a group of numbers.

2. How to Find the Average of the given numbers?

Example Problem

The marks obtained by 8 students in a class test are 12, 15, 16, 18, 20, 10, 11, and 21. Use the Average formula and find out what the Average of the marks obtained by the students is.

Solution:

Marks obtained by 8 students in class test = 12, 15, 16, 18, 20, 10, 11, and 21 (given)

Total marks obtained by 8 students in class test =(12+15+16+18+20+10+11+21) = 123/8

Using the Average formula,

Average = (Sum of Observation) ÷ (Total numbers of Observations)

Average = (12+15+16+18+20+10+11+21) ÷ 8

Average = 123/8

Average of marks obtained by 8 students = 15.375

3. Rules of Average

Here are some handy tricks for Average which will make your calculation faster and more efficient with practice:

(1) If the value of each number is increased by the same value 'a', then the Average of all numbers will also increase by 'a'.

(2) If the value of each number is decreased by the same value 'a', then the Average of all numbers will also decrease by 'a'.

(3) If the value of each number is multiplied by the same value 'a', then the Average of all numbers will also get multiplied by 'a'.

(4) If the value of each number is divided by the same value 'a', then the Average of all numbers will also get divided by 'a'.

4. Average of two or more groups taken together

(a) If the number of quantities in two groups is n₁ and n₂ and their Average is x and Y, respectively, the combined Average (Average of all of them put together) is =(n₁ x+n₂ Y)/(n₁+n₂ )

(b) If the Average of ₁ quantities is x and the Average of n₂ quantities out of them is Y, the average of the remaining group (rest of the quantities) is =(n₁ x-n₂ Y)/(n₁ – n₂ )

5. What is Average Speed?

Average Speed is the rate at which a journey takes place. Throughout a journey, the Speed is not constant; it varies from time to time.

Average Speed Formula

The Average Speed of an object is equal to the total distance covered by the object, divided by the total time taken to cover the distance.

Average Speed = Total distance covered ÷ Total time taken.

S = D/T.

Where

'D' is the distance travelled in some time 'T'

'S' is the Speed of the object for this journey.