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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.4



 



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,



Statistics – Exercise – 32.7 – Q.8



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,



Statistics – Exercise – 32.7 – Q.8(i)



∴  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.9



 



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
		

	




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
		

	







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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