Study Notes On Average Formula With Examples

Average Formula

What is Average?

In maths, Average is the calculated “central” value of a set of numbers. The term ‘average’ refers to the ‘middle’ or ‘central’ point. In simple words, Average refers to a number that is a typical representation of a set of data. In Mathematics, Average is defined as the mean value which is equal to the ratio of the sum of all the data to the total no. of values/units present in the set. For example, the average of 3, 6, and 9 is 2 + 7 + 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.

Average Symbol

• We can define average as the mean of the values which are represented by x̄ (x bar) also known as the average symbol.

• The average symbol also denoted by ‘μ’.

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 helps to give an estimate of the rate at which the journey is completed. Let’s find out more about Average Speed.

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. When ‘D’ is the distance traveled in some time ‘T’ and the speed of the object for this journey or ‘s’ is equal to

Average Speed = Total distance covered ÷ Total time taken

s = D/T.

Average Speed Formula Examples

Q. The average weight of 24 students of section A of a class is 58 kg whereas the average weight of 26 students of section B of the same class is 60.5 kg. Find the average weight of all the 50 students of the class.

Sol. Here n₁ = 24, n₂ = 26, x = 58 and y = 60.5.
∴ Average weight of all the 50 students
=(n₁ x+n₂ y)/(n₁+n₂ )
=(24×58+24×60.5)/(24+26)
=(1392+1573)/50=2965/50
= 59.3 kg

• The average of n quantities is equal to x. If one of the given quantities whose value is p, is replaced by a new quantity having value q, the average becomes y,  then

Q. The average weight of 25 persons is increased by 2 kg when one of them whose weight is 60 kg is replaced by a new person. What is the weight of the new person?

Sol. The weight of the new person
= p + n(y – x)
= 60 + 25(2) = 110 kg

• 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

Q. The average age of 24 students and the class teacher is 16 years. If the class teacher’s age is excluded, the average age reduces by 1 year. What is the age of the class teacher?

Sol. The age of class teacher
= n (x – y) + y
= 25 (16 – 15) + 15
= 40 years

• The average of first n natural numbers is

• The average of square of natural numbers till n is

• The average of cubes of natural numbers till n is

• The average of odd numbers from 1 to n is

• The average of even numbers from 1 to n is

Click Here to Attempt More Questions From Quantitative Aptitude For SSC CGL 

Q. What is the average of odd numbers from 1 to 40?

Sol. The required average
=(last odd number+1)/2
=(39+1)/2
= 20

Q. What is the average of even numbers from 1 to 81?

Sol. The required average
=(last even number+2)/2
=(80+2)/2
= 41

• If n is odd: The average of n consecutive numbers, consecutive even numbers or consecutive odd numbers is always the middle number.

• If n is even: The average of n consecutive numbers, consecutive even numbers or consecutive odd numbers is always the average of the middle two numbers.

• The average of first n consecutive even numbers is   (n + 1)

• The average of first n consecutive odd numbers is n.

•  The average of squares of first n consecutive even numbers is

• The average of squares of consecutive even numbers till n is

• The average of squares of consecutive odd numbers till n is

• If the average of n consecutive number is m, then the difference between the smallest and the largest number if

Q. Find the average of squares of first 19 consecutive even numbers.

Sol. The required average
=(2 (n+1)(2n+1))/3=(2(19+1)(2×19+1))/3
=(2×20×39)/3=1560/3=520

Q. Find the average of squares of consecutive odd numbers from 1 to 31. 

Sol. The required average
=(n (n+2))/3=(31×(31+2))/3=(31×33)/3=341

Q Find the average velocity when the changes in displacement in three consecutive instances are 8 m, 10 m, 12 m, and the total time taken is 6 s.

Explanation: The total change in displacement = 30 m that is, (8+10+12). Now, the total time is taken = 6 s. Therefore, the Average velocity = total change in displacement/total time taken = 30/6 = 5 m/s.