Q.1: Find the
average of the following set of numbers. 65, 85, 70, 90, and 105.
Solution: Given, the set of numbers is
65, 85, 70, 90, and 105.
Average = Sum of
numbers/total numbers
Average =
(65+85+70+90+105)/5
= 415/5
= 83
Q.2: The sum
of 10 numbers is 550. Find their average number.
Solution: Given, the sum of 10 numbers
is 550.
Average = Sum/Total
numbers
= 550/10
= 55
Q.3: What is
the average of natural numbers from 1 to 67?
Solution: Given, natural numbers 1 to
67.
Average of n natural
numbers = (n+1)/2
Here, n = 67
Average = (67+1)/2 = 68/2 = 34
Q.4: The
average of 7 consecutive numbers is 20. What is the largest of these numbers?
Solution: Let the 7 consecutive
numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
As per the given
condition;
[x + (x + 1) + (x + 2) +
(x + 3) + (x + 4) + (x + 5) + (x + 6)] / 7 = 20
⇒ 7x + 21 = 140
⇒ 7x = 119
⇒ x =17
The largest number = x + 6 = 23.
Q.5: The
average of 10 numbers is 23. If each number is increased by 4, what will the
new average be?
Solution: Given,
Average of 10 numbers = 23
Sum/Total numbers = 23
Sum/10 = 23
Sum of the 10 numbers =
230
If each number is
increased by 4, the total increase = 4 x 10 = 40
New sum = 230 + 40 = 270
Therefore, the new average = 270/10 =
27
Q.6: The
average of 50 numbers is 20. If two numbers 37 and 43 are discarded, find the
average of the remaining numbers.
Solution: Given,
Average of 50 numbers = 20
Sum of 50 numbers = 20 x
50 = 1000
Sum of discarded numbers =
37 + 43 = 80
Sum of remaining numbers =
1000 – 80 = 920
Now, total remaining
numbers = 50 – 2 = 48
Average of remaining numbers = 920/48
= 19.17
Q.7: What is
the average of the first six multiples of 4?
Solution: First six multiples of 4 is
4, 8, 12, 16, 20, 24
Average =
(4+8+12+16+20+24)/6
= 84/6
= 14
Q.8: The
average age of three boys is 15 years and their ages are in proportion 3:5:7.
What is the age in years of the youngest boy?
Solution: Let the age of the youngest
boy be x.
As per the question;
(3x+5x+7x)/3 = 15
3x+5x+7x = 45
15x = 45
x = 45/15
x = 3
Age of the youngest boy is: 3x = 3(3)
= 9 years
Q.9: The
average weight of a group of seven boys is 56 kg. The individual weights (in
kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the
seventh boy.
Solution: Average weight of 7 boys =
56 kg.
Total weight of 7 boys =
(56 × 7) kg = 392 kg.
Total weight of 6 boys =
(52 + 57 + 55 + 60 + 59 + 55) kg
= 338 kg.
Weight of the 7th boy =
(total weight of 7 boys) – (total weight of 6 boys)
= (392 – 338) kg
= 54 kg.
Therefore, the weight of the seventh
boy is 54 kg.
Q.10: The
mean of 25 numbers is 36. If the mean of the first numbers is 32 and that of
the last 13 numbers is 39, find the 13th number.
Solution:
Mean of the first 13
numbers = 32
Sum of the first 13
numbers = (32 × 13) = 416
Mean of the last 13
numbers = 39
Sum of the last 13 numbers
= (39 × 13) = 507
Mean of 25 numbers = 36
Sum of all the 25 numbers
= (36 × 25) = 900
Therefore, the 13th
observation = (416 + 507 – 900) = 23
Hence, the 13th
observation is 23
1.
Find
the average of 5 multiples of 10.
2.
Find
the average of the first 10 odd numbers.
3.
Find
the average of the first 10 even numbers.
