**Question 1.The means of two samples of sizes 60 and 120 respectively are 35.4 and 30.9 and the standard deviations are 4 and 5. Obtain the standard deviation of the sample of size 180 obtained by combining the two samples.Solution:**

**Question 2.For certain 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:85, 91, 96, 88, 98, 82Solution:**

**Question 4.Find the coefficient of variation of a sample that has a mean equal to 25 and a standard deviation of 5.Solution:**

**Question 5.A group of 65 students of class XI has their average height as 150.4 cm with a coefficient of variance of 2.5%. What is the standard deviation of their heights?Solution:**

∴ The standard deviation of students’ height is 3.76 cm.

**Question 6.Two workers on the same job show 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

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.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),

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 two classes. Calculate the coefficient of variation of the two distributions. Which series is more variable?Solution:**

Let x denote the data of class A and y denote the data of class B.

Calculation of S.D. for class A:

Since C.V. (Y) > C.V.(X),

C.V. (B) > C.V. (A)

∴ Series B is more variable.

**Question 9.Compute the coefficient of variation for team A and team B.Which team is more consistent?Solution:**

Let denote no. of goals of team A and 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.