Selina Concise Class 10 Math Chapter 24 Exercise 24A Measures of Central Tendency Solutions
Measures of Central Tendency
Exercise – 24A
(Q1) Find the mean of the following set of numbers:
(i) 6, 9, 11, 12 and 7
Solution:
Total set of numbers are 5.
∴ n = 5
We know that, the formula of mean is –
Mean = Σ x/n
First we have to find –
Σ x = 6+9+11+12+7
Σ x = 45
∴ Mean = 45/5
Mean = 9
(ii) 11, 14, 23, 26, 10, 12, 18 and 6.
Solution:
Total set of numbers are 8.
∴ n = 8
We know that, the formula of mean is –
Mean = Σ x/n
First we have to solve –
Σ x = 11+14+23+26+10+12+18+6
Σ x = 120
∴ Mean = 120/8
Mean = 15
(Q2) Marks obtained (in mathematics) by 9 students are given below.
60, 67, 52, 76, 50, 51, 74, 45 and 56
(a) Find the arithmetic mean.
(b) If marks of each student be increased by 4; what will be the new value of arithmetic mean.
Solution:
Given, the marks obtained by 9 students are –
60, 67, 52, 76, 50, 51, 74, 45, and 56
(a) We have to find arithmetic mean –
∴ n = 9 (Number of students)
We know that,
Mean = Σ x/n
First we have to solve –
Σ x = 60+67+52+76+50+51+74+45+56
Σ x = 531
∴ Mean = 531/9
Mean = 59
∴ Arithmetic mean = 59
(b) If marks of each student be increased by 4.
Σ x = 64+71+56+80+54+55+78+49+60
= 567
∴ New arithmetic mean = Σ x/n
= 567/9
= 63
(Q3) Find the mean of the natural numbers from 3 to 12
Solution:
First we have to write natural numbers from 3 to 12.
3, 4, 5, 6, 7, 8, 9, 10, 11 and 12
Total natural numbers are 10.
∴ n = 10
We know that,
Mean = Σ x/n
First we have to solve Σ x –
Σ x = 3+4+5+6+7+8+9+10+11+12
Σ x = 75
∴ Mean = 75/10
Mean = 75
(Q4) (a) Find the mean of 7, 11, 6, 5 and 6.
Solution:
Given, the numbers are 7, 11, 6, 5 and 6
Total numbers are 5.
∴ n = 5
We know that,
Mean = Σ x/n
Firs we have to find Σ x –
Σ x = 7+11+6+5+6
Σ x = 35
Mean = 35/5
Mean = 7
(b) If each number given in (a) is diminished by 2, find the new value 6F mean.
Solution:
The given numbers are 7, 11, 6, 5 and 6.
In this number subtracted by 2 in each number
7-2 = 5, 11-2 = 9, 6-2 = 4, 5-2 = 3, 6-2 = 4
The new numbers are –
5, 9, 4, 3, 4
∴ n = 5
Mean = Σ x/n
= 5+9+4+3+4/5
= 25/5
Mean = 5
(Q5) If the mean of 6, 4, 7, ‘a’ and 10 is 8. Find the value of ‘a’
Solution:
Given that, the number of terms are –
6, 4, 7, a and 10
∴ n = 5
Also, given that,
Mean = 8
We know that,
Mean = Σ x/n
∴ Σ x = mean × n
= 8 × 5
Σ x = 40 —- (1)
and Σ x = 6+4+7+a+10
Σ x = 27+a —- (2)
From equation (1) and (2),
40 = 27 + a
40 – 27 = a
13 = a
∴ a = 13
(Q6) The mean of the number 6, ‘y’, 7, ‘x’ and 14 is 8.
Express ‘y’ in terms of ‘x’
Solution:
Given number of terms 6, y, 7, x and 14.
Given that: mean = 8 and
∴ n = 5
We know that
Mean = Σ x/n
Mean × n = Σ x
Σ x = mean × n
= 8 × 5
Σ x = 40 —– (1)
∴ Σ x = 6+y+7+x+14
Σ x = 27+y+x —– (2)
From equation (1) and (2)
40 = 27 + y + x
40 – 27 = y + x
13 = y + x
∴ y = 13 – x
Here is your solution of Selina Concise Class 10 Math Chapter 24 Exercise 24A Measures of Central Tendency
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