Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 2 Measures of Dispersion Ex 2.3 Questions and Answers.

Maharashtra State Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3

Question 1.
The mean and standard deviation of two distributions of 100 and 150 items are 50, 5, and 40, 6 respectively. Find the mean and standard deviation of all the 250 items taken together.
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q1
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q1.1
∴ The mean and standard deviation of all 250 items taken together are 44 and √55.6 respectively.

Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3

Question 2.
For certain bivariate data, the following information is available.
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q2
Obtain the combined standard deviation.
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q2.1
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q2.2

Question 3.
Calculate the coefficient of variation of marks secured by a student in the exam, where the marks are: 2, 4, 6, 8, 10. (Given: √8 = 2.8284)
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q3
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q3.1

Question 4.
Find the coefficient of variation of a sample that has a mean equal to 25 and a standard deviation of 5.
Solution:
Given, \(\bar{x}\) = 25, σ = 5
C.V. = 100 × \(\frac{\sigma}{\bar{x}}\)
= 100 × \(\frac{5}{25}\)
= 20%

Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3

Question 5.
A group of 65 students of class XI has their average height as 150.4 cm with a coefficient of variation of 2.5%. What is the standard deviation of their height?
Solution:
Given, n = 65, \(\bar{x}\) = 150.4, C.V. = 2.5%
C.V. = 100 × \(\frac{\sigma}{\bar{x}}\)
∴ 2.5 = 100 × \(\frac{\sigma}{150.4}\)
∴ \(\frac{2.5 \times 150.4}{100}\) = σ
∴ σ = 3.76
∴ the standard deviation of students’ height is 3.76.

Question 6.
Two workers on the same job show1 the following results:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q6
(i) Regarding the time required to complete the job, which worker is more consistent?
(ii) Which worker seems to be faster in completing the job?
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q6.1
(i) Since, C.V. (P) < C.V.(Q)
∴ Worker P is more consistent regarding the time required to complete the job.

(ii) Since, \(\bar{p}\) > \(\bar{q}\)
i.e., the expected time for completing the job is less for worker Q.
∴ Worker Q seems to be faster in completing the job.

Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3

Question 7.
A company has two departments with 42 and 60 employees respectively. Their average weekly wages are ₹ 750 and ₹ 400. The standard deviations are 8 and 10 respectively.
(i) Which department has a larger bill?
(ii) Which department has larger variability in wages?
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q7
(i) Since, \(\bar{x}_{1}>\bar{x}_{2}\)
i.e., average weekly wages are more for the first department.
∴ the first department has a larger bill.
(ii) Since, C.V. (1) < C.V. (2)
∴ the second department is less consistent.
∴ the second department has larger variability in wages.

Question 8.
The following table gives the weights of the students of class A. Calculate the coefficient of variation (Given √8 = 0.8944)
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q8
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q8.1
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q8.2

Question 9.
Compute coefficient of variation for team A and team B. (Given: √2.5162 = 1.5863, √2.244 = 1.4980)
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q9
Which team is more consistent?
Solution:
Let f1 denote no. of goals of team A and f2 denote no. of goals of team B.
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q9.1
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q9.2
Since C.V. of team A > C.V. of team B.
∴ team B is more consistent.

Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3

Question 10.
Given below is the information about marks obtained in Mathematics and Statistics by 100 students in a class. Which subject shows the highest variability in marks?
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q10
Solution:
Maharashtra Board 11th Commerce Maths Solutions Chapter 2 Measures of Dispersion Ex 2.3 Q10.1
Since C.V. (S) > C.V. (M)
∴ The subject statistics show higher variability in marks.