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:

∴ The mean and standard deviation of all 250 items taken together are 44 and √55.6 respectively.

Question 2.

For certain bivariate data, the following information is available.

Obtain the combined standard deviation.

Solution:

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:

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%

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:

(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:

(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.

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:

(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)

Solution:

Question 9.

Compute coefficient of variation for team A and team B. (Given: √2.5162 = 1.5863, √2.244 = 1.4980)

Which team is more consistent?

Solution:

Let f_{1} denote no. of goals of team A and f_{2} denote no. of goals of team B.

Since C.V. of team A > C.V. of team B.

∴ team B is more consistent.

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?

Solution:

Since C.V. (S) > C.V. (M)

∴ The subject statistics show higher variability in marks.