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Chapter 32: Statistics – Exercise 32.7

Statistics – Exercise – 32.7 – Q.1

We observe that the average monthly wages in both firms is same i.e. Rs. 2500. Therefore the plant with greater variance will have greater variability.

Thus plant B has greater variability in individual wages.

 

Statistics – Exercise – 32.7 – Q.2

We observe that the average weights and heights for the 50 students is same i.e. 63.2.

Therefore, the parameter with greater variance will have more variability.

Thus, height has greater variability than weights.

 

Statistics – Exercise – 32.7 – Q.3



So, we have:



 

Statistics – Exercise – 32.7 – Q.4


	
		
	
	

		

			
CI
			
f
			
x
			
u = (x – A)/h
			
fu
			
u2
			
fu2
		
		

			
1000 – 1700
			
12
			
1350
			
-2
			
-24
			
4
			
48
		
		

			
1700 – 2400
			
18
			
2050
			
-1
			
-18
			
1
			
18
		
		

			
2400 – 3100
			
20
			
2750
			
0
			
0
			
0
			
0
		
		

			
3100 – 3800
			
25
			
3450
			
1
			
25
			
1
			
25
		
		

			
3800 – 4500
			
35
			
4150
			
2
			
70
			
4
			
140
		
		

			
4500 – 5200
			
10
			
4850
			
3
			
30
			
9
			
90
		
		

			
 
			
120
			
 
			
 
			
83
			
 
			
321
		
	


Here, 



 

Statistics – Exercise – 32.7 – Q.5

(i) Total wages paid by firm A = (Average wages) × (Number of employees)

= 52.5 × 587 = Rs 30817.50

Total wages paid by firm B = (Average wages) × (Number of employees)

= 47.5 × 648 = Rs 30780

So, firm A pays higher total wages,

(ii) In order to compare the variability of wages among the two firms, we have to calculated their coefficients of variation.

Let σ1 and σ2 denote the standard deviations of Firm A and Firm B respectively. Further,

letbe the mean wages in firms A and B respectively.

We have,



Now,

Coefficient of variation in wages in firm



and,

Coefficient of variation in wages in firm



Clearly, coefficient of variation in wages in greater for firm B than for firm A.

So, firm B shows more variability in wages.

 

Statistics – Exercise – 32.7 – Q.6

In order to compare the variability of weight in boys and girls, we have to calculate their coefficients of variation.

Let σ1 and σ2 denote the standard deviations of weight in boys and girls respectively. Further,

letbe the mean weight of boys and girls respectively.

we have,



Now,

Coefficient of variation in weights in boys



and,

Coefficient of variation in weights in girls



Clearly, Coefficient of variation in weights is greater in boys than in girls.

So, weights shows move variability in boys.

 

Statistics – Exercise – 32.7 – Q.7

In order to compare the variability of marks in Math, Physics, and Chemistry, we have to calculate their coefficients of variation.

Let σ1, σ2 and σ3 denote the standard deviations of marks in Math, Physics and chemistry respectively.

Further, letbe the mean scores in Math, Physics and Chemistry respectively.

We have,



Now,

Coefficient of variation in Maths



Coefficient of variation in Physics



Coefficient of variation in Chemistry



Clearly, Coefficient of variation in marks is greatest in Chemistry and lowest in Math.

So, marks in chemistry show highest variability and marks in maths show lowest variability.

 

Statistics – Exercise – 32.7 – Q.8

Let's first find the cofficient of variable for Group G1


	
		
		
		
	
	

		

			
CI
			
f
			
x
			
u = (x - A)/h
			
fu
			
u2
			
fu2
		
		

			
10 – 20
			
9
			
15
			
-3
			
- 27
			
9
			
81
		
		

			
20 – 30
			
17
			
25
			
-2
			
- 34
			
4
			
68
		
		

			
30 – 40
			
32
			
35
			
-1
			
- 32
			
1
			
32
		
		

			
40 – 50
			
33
			
45
			
0
			
0
			
0
			
0
		
		

			
50 – 60
			
40
			
55
			
1
			
40
			
1
			
40
		
		

			
60 – 70
			
10
			
65
			
2
			
20
			
4
			
40
		
		

			
70 – 80
			
9
			
75
			
3
			
27
			
9
			
81
		
		

			
 
			
150
			
 
			
 
			
-6
			
 
			
342
		
	


Here,



Now, let's find the coefficient of variable for Group G2


	
		
		
		
		
	
	

		

			
CI
			
f
			
x
			
u = (x – A)/h
			
fu
			
u2
			
fu2
		
		

			
10 – 20
			
10
			
15
			
-3
			
30
			
9
			
90
		
		

			
20 – 30
			
20
			
25
			
-2
			
40
			
4
			
80
		
		

			
30 – 40
			
30
			
35
			
-1
			
30
			
1
			
30
		
		

			
40 – 50
			
25
			
45
			
0
			
0
			
0
			
0
		
		

			
50 – 60
			
43
			
55
			
1
			
43
			
1
			
43
		
		

			
60 – 70
			
15
			
65
			
2
			
30
			
4
			
60
		
		

			
70 – 80
			
7
			
75
			
3
			
21
			
9
			
63
		
		

			
 
			
150
			
 
			
 
			
-6
			
 
			
366
		
	


Here,



∴  Group G2 is more variable.

 

Statistics – Exercise – 32.7 – Q.9


	
		
		
		
		
		
	
	

		

			
CI
			
f
			
x
			
u = (x - A)/h
			
fu
			
u2
			
fu2
		
		

			
10 – 15
			
2
			
12.5
			
-2
			
-4
			
4
			
8
		
		

			
15 – 20
			
8
			
17.5
			
-1
			
-8
			
1
			
8
		
		

			
20 – 25
			
20
			
22.5
			
0
			
0
			
0
			
0
		
		

			
25 – 30
			
35
			
27.5
			
1
			
35
			
1
			
35
		
		

			
30 – 35
			
20
			
32.5
			
2
			
40
			
4
			
80
		
		

			
35 – 40
			
15
			
37.5
			
3
			
45
			
9
			
135
		
		

			
 
			
100
			
 
			
108
			
 
			
 
			
266
		
	


Here,



 

Statistics – Exercise – 32.7 – Q.10


	
		
		
		
	
	

		

			
 x
			
d = (x – Mean)
			
 d2
		
		

			
35
			
-13
			
169
		
		

			
24
			
-24
			
576
		
		

			
52
			
4
			
16
		
		

			
53
			
5
			
25
		
		

			
56
			
8
			
64
		
		

			
58
			
10
			
100
		
		

			
52
			
4
			
16
		
		

			
50
			
2
			
4
		
		

			
51
			
3
			
9
		
		

			
49
			
1
			
1
		
		

			
480
			
 
			
980
		
	





	
		
		
		
	
	

		

			
x
			
d = (x – Mean)
			
  d2
		
		

			
35
			
-13
			
169
		
		

			
24
			
-24
			
576
		
		

			
52
			
4
			
16
		
		

			
53
			
5
			
25
		
		

			
56
			
8
			
64
		
		

			
58
			
10
			
100
		
		

			
52
			
4
			
16
		
		

			
50
			
2
			
4
		
		

			
51
			
3
			
9
		
		

			
49
			
1
			
1
		
		

			
480
			
 
			
980
		
	




Since the coefficient of variation for shares Y is smaller than the coefficient of variation for shares X, they are more stable.

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