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.