Average is calculated by adding all the observations and dividing the sum by number of observations.
Average is also known as arithmetic mean

Important Formulae:-

Sum of observations = Average x no. of observations

2.Average of first 'n' natural numebrs:

3.Average of Square of first ‘n’ natural numbers =

4.Average of cube of natural numbers =

5.Sum of first ‘n’ odd numbers is  = n²

6.Sum of first ‘n’ even numbers is = n²+n

7.If average of some numbers is ‘x’ and a constant number ‘a’ is added to each term of the series, then new average = x+a

8.If average of some numbers is ‘x’ and a constant number ‘a’ is subtracted from each term of the series then, new average = x-a

9.If average of some numbers is ‘x’ and each term of the series is multiplied by a constant number ‘a’ then new average = ax

10.If average of some numbers is ‘x’ and each term of the series is divided by a constant number ‘a’ then new average = x/a

11.In Replacement case :-
Weight of new person = weight of outgoing person + no. of persons (inc. average)
(OR)
=weight of outgoing person – no. of persons (dec.average)
Non Replacement case :-
Teacher age = existing average + no. of persons (inc. average)
(OR)
=Existing Average – no. of persons (dec.average)

Practice following examples

1)Average of 14 quantities is 22 and average of 36 quantities is 25. What is the average of all the 50 quantities?

1) 28.32 2)23.16 3)24.16 4)22.08 5) None of these

Ans:24.16

Hint:Sum of observations /no. of observations (308+900 / 50)

2)The average of 42 observations is 36 and average of 18 observations is 24. What is the average of all the 60 observations?

1)28.5 2)37.6 3)32.4 4)21.52 5)None of thes

Ans:32.4

Hint:Sum of observations /no. of observations (1512 + 432 /60)

3)The average marks obtained by Ram in Maths & Science were 30 less than his marks in Maths. He got 60 marks in science. Find his marks in Maths?

1)122 2)120 3)124 4)102 5)None of these

Ans:122

4)The average age of 24 students is 12 years. If the age of teacher is added, the average will be increased by 1 year. What is the age of the teacher?

1)35 years 2) 37 years 3)27 years 4)30 years 5) None of these

Ans:37 years

Hint:25*13=325 - 24*12=288

5)The average of 26 numbers is 22. If each number is increased by 8. What will be the new average?

1) 34 2)29 3)30 4)32 5)None of these

Ans:30

• Prev
• Next