Maharashtra State Board 11th Maths Solutions Chapter 8 Measures of Dispersion Ex 8.3
Question 1
Maharashtra Board Solution
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 & Step-by-Step Answer:
Question 2
Maharashtra Board Solution
For certain data, the following information is available. Obtain the combined standard deviation.
Solution & Step-by-Step Answer:
Question 3
Maharashtra Board Solution
Calculate the coefficient of variation of marks secured by a student in the exam, where the marks are: 85, 91, 96, 88, 98, 82
Solution & Step-by-Step Answer:
Question 4
Maharashtra Board Solution
Find the coefficient of variation of a sample that has a mean equal to 25 and a standard deviation of 5.
Solution & Step-by-Step Answer:
Question 5
Maharashtra Board Solution
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 & Step-by-Step Answer:
Given, n = 65, = 150.4, C.V. = 2.5% ∴ The standard deviation of students’ height is 3.76 cm.
Question 6
Maharashtra Board Solution
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 & Step-by-Step Answer:
(i) Since C.V. (P) < C.V.(Q), Worker P is more consistent regarding the time required to complete the job. (ii) Since , 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
Maharashtra Board Solution
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 & Step-by-Step Answer:
(i) Since , 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
Maharashtra Board Solution
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 & Step-by-Step Answer:
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
Maharashtra Board Solution
Compute the coefficient of variation for team A and team B. Which team is more consistent?
Solution & Step-by-Step Answer:
Let f1 denote no. of goals of team A and f2 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
Maharashtra Board Solution
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 & Step-by-Step Answer:
Since C.V. (S) > C.V. (M), The subject statistics show higher variability in marks.
