NCERT Solutions class-11 Maths Exercise 15.3

Exercise 15.3

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

Ans. Group A

Mean

= = 45 – 0.4 = 44.6

Standard deviation

=

= = = 15.09

Group B

Mean

= = 45 – 0.4 = 44.6

Standard deviation

=

=

= = 15.61

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

Ans.

Mean = 51and Mean 105

= = 5.92 and = = 2

C.V. of = = 11.61andC.V. of = = 1.9

C.V. of Y < C.V. of X

Therefore, prices of share Y are more stable.

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

Firm A Firm B

No. of wage earners 586 648

Mean of monthly wages Rs. 5253Rs. 5253

Variance of the distribution of wages 100 121

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

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

Ans. (i) Firm A: Number of wages earners = 586

Mean of monthly wages = Rs. 5253

Total money wages = = Rs. 3078258

Firm B: Number of wages earners = 648

Mean of monthly wages = Rs. 5253

Total money wages = = Rs. 3403944

(ii) Since both the firms have same mean of monthly wages, so the firm with greater variance will have more variability in individual wages. Thus firm B will have more variability in individual wages.

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4. 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?

Ans. Team A

Mean = = 2

Standard deviation =

= = = 1.09

C.V. of Team A = = 54.5 and C.V. of Team B = = 62.5

Here, C.V. of Team A < C.V. of team B

Therefore, team A is more consistent.

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

Which is more varying, the length or weight?

Ans. Given:

= 4.24

= 18.056 – 17.978 = 0.078

= 0.28

Also = 5.22

= 29.152 – 27.248 = 1.904

= 1.38

C.V. of length = = 6.6 and C.V. of weight =

Here, C.V of weight > C.V. of length

Therefore, weights have more variability than lengths.