Balbharati Maharashtra State Board11th Commerce Maths Solution Book PdfChapter 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
Maharashtra Board Solution
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 & Step-by-Step Answer:
∴ The mean and standard deviation of all 250 items taken together are 44 and √55.6 respectively.
Question 2
Maharashtra Board Solution
For certain bivariate 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: 2, 4, 6, 8, 10. (Given: √8 = 2.8284)
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:
Given, = 25, σ = 5 C.V. = 100 × = 100 × = 20%
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 variation of 2.5%. What is the standard deviation of their height?
Solution & Step-by-Step Answer:
Given, n = 65, = 150.4, C.V. = 2.5% C.V. = 100 × ∴ 2.5 = 100 × ∴ = σ ∴ σ = 3.76 ∴ the standard deviation of students’ height is 3.76.
Question 6
Maharashtra Board Solution
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 & 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) ∴ the 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 class A. Calculate the coefficient of variation (Given √8 = 0.8944)
Solution & Step-by-Step Answer:
Question 9
Maharashtra Board Solution
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 & 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.
