NCERT Solutions for Class 11 Maths chapter 15-Statistics Exercise 15.3

NCERT Solutions for Class-11 Maths Chapter-15 Statistics

NCERT Solutions for Class 11 Maths Chapter-15 Statistics Exercise 15.3 prepared by the expert of Physics Wallah score more with Physics Wallah NCERT Class 11 maths solutions. You can download and share NCERT Solutions for Class 11 Maths.

 

NCERT Solutions for Class-11 Maths Exercise 15.3

Question1. From the data given below state which group is more variable, A or B?

Solution :
Group A

 

Where A = 45,

and y_i = (x_i – A)/h

Here h = class size = 20 – 10

h = 10

So, x̅ = 45 + ((-6/150) × 10)

= 45 – 0.4

= 44.6

 

 

 

σ² = (10²/150²) [150(342) – (-6)²]

= (100/22500) [51,300 – 36]

= (100/22500) × 51264

= 227.84

Hence, standard deviation = σ = √227.84

= 15.09

∴ C.V for group A = (σ/ x̅) × 100

= (15.09/44.6) × 100

= 33.83

Group B

 

Where A = 45,

h = 10

So, x̅ = 45 + ((-6/150) × 10)

= 45 – 0.4

= 44.6

 

 

σ² = (10²/150²) [150(366) – (-6)²]

= (100/22500) [54,900 – 36]

= (100/22500) × 54,864

= 243.84

Hence, standard deviation = σ = √243.84

= 15.61

∴ C.V for group B = (σ/ x̅) × 100

= (15.61/44.6) × 100

= 35

By comparing C.V. of group A and group B.

C.V of Group B > C.V. of Group A

So, Group B is more variable.

Question2. From the prices of shares X and Y below, find out which is more stable in value:

Solution :

We have to calculate Mean for x,

Mean x̅ = ∑x_i/n

Where, n = number of terms

= 510/10

= 51

 

= (1/10²)[(10 × 26360) – 510²]

= (1/100) (263600 – 260100)

= 3500/100

= 35

WKT Standard deviation = √variance

= √35

= 5.91

So, co-efficient of variation = (σ/ x̅) × 100

= (5.91/51) × 100

= 11.58

Now, we have to calculate Mean for y,

Mean ȳ = ∑y_i/n

Where, n = number of terms

= 1050/10

= 105

 

 

= (1/10²)[(10 × 110290) – 1050²]

= (1/100) (1102900 – 1102500)

= 400/100

= 4

WKT Standard deviation = √variance

= √4

= 2

So, co-efficient of variation = (σ/ x̅) × 100

= (2/105) × 100

= 1.904

By comparing C.V. of X and Y.

C.V of X > C.V. of Y

So, Y is more stable than X.

 

Question3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

Solution :
(i) Monthly wages of firm A = Rs 5253

Number of wage earners in firm A = 586

∴Total amount paid = Rs 5253 × 586

Monthly wages of firm B = Rs 5253

Number of wage earners in firm B = 648

∴Total amount paid = Rs 5253 × 648

Thus, firm B pays the larger amount as monthly wages as the number of wage earners in firm B are more than the number of wage earners in firm A.

(ii) Variance of firm A = 100

We know that, standard deviation (σ)= √100

=10

Variance of firm B = 121

Then,

Standard deviation (σ)=√(121 )

=11

Hence the standard deviation is more in case of Firm B that means in firm B there is greater variability in individual wages.

Question4. The following is the record of goals scored by team A in a football session:

For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?

Solution :
The mean and the standard deviation of goals scored by team A are calculated as follows.

Question5. The sum and sum of squares corresponding to lengths x(in cm) and weight y(in gm) of 5- plant products are given below:

Which is more varying, the length or weight?

Solution :
Given: