# Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 2 - Measures of Dispersion [Latest edition]

## Chapter 2: Measures of Dispersion

Exercise 2.1Exercise 2.2Exercise 2.3Miscellaneous Exercise 2
Exercise 2.1 [Pages 26 - 27]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 2 Measures of Dispersion Exercise 2.1 [Pages 26 - 27]

Exercise 2.1 | Q 1 | Page 26

Find range of the following data:
575, 609, 335, 280, 729, 544, 852, 427, 967, 250

Exercise 2.1 | Q 2 | Page 26

The following data gives number of typing mistakes done by Radha during a week. Find the range of the data:

 Day Monday Tuesday Wednesday Thursday Friday Saturday No. of mistake 15 20 21 12 17 10
Exercise 2.1 | Q 3 | Page 26

Find range of the following data.

 Classes 62 – 64 64 – 66 66 – 68 68 – 70 70 – 72 Frequency 5 3 4 5 3
Exercise 2.1 | Q 4 | Page 26

Find the Q.D. for the following data.
3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3.

Exercise 2.1 | Q 5 | Page 26

Given below are the prices of shares of a company for the last 10 days. Find Q.D.: 172, 164, 188, 214, 190, 237, 200, 195, 208, 230.

Exercise 2.1 | Q 6 | Page 26

Calculate Q. D. for the following data:

 X 24 25 26 27 28 29 30 F 6 5 3 2 4 7 3
Exercise 2.1 | Q 7 | Page 26

Following data gives the age distribution of 250 employees of a firm. Calculate Q.D. of the distribution:

 Age(in years) 20 – 25 25 – 30 30 – 35 35 – 40 40 – 45 45 – 50 No. of employees 30 40 60 50 46 14
Exercise 2.1 | Q 8 | Page 27

Following data gives the weight of boxes.
Calculate Q.D. for the data:

 Weight (kg.) 10 – 12 12 – 14 14 – 16 16 – 18 18 – 20 20 – 22 No. of boxes 3 7 16 14 18 2 c.f. 3 10 26 40 58 60
Exercise 2.2 [Pages 30 - 31]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 2 Measures of Dispersion Exercise 2.2 [Pages 30 - 31]

Exercise 2.2 | Q 1 | Page 30

Find the various and S.D. for the following set of numbers.
7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 8, 2, 6

Exercise 2.2 | Q 2 | Page 30

Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129

Exercise 2.2 | Q 3 | Page 31

Compute variance and standard deviation for the following data:

 x 2 4 6 8 10 f 5 4 3 2 1
Exercise 2.2 | Q 4 | Page 31

Compute the variance and S.D.

 x 1 3 5 7 9 Frequency 5 10 20 10 5
Exercise 2.2 | Q 5 | Page 31

Following data gives age of 100 students in a school. Calculate variance and S.D.

 Age (In years) 10 11 12 13 14 No. of students 10 20 40 20 10
Exercise 2.2 | Q 6 | Page 31

The mean and variance of 5 observations are 3 and 2 respectively. If three of the five observations are 1, 3 and 5, find the values of other two observations.

Exercise 2.2 | Q 7 | Page 31

Obtain standard deviation for the following date:

 Height (in inches) 60 – 62 62 – 64 64 – 66 66 – 68 68 – 70 Number of students 4 30 45 15 6
Exercise 2.2 | Q 8 | Page 31

The following distribution was obtained change of origin and scale of variable X.

 di – 4 – 3 – 2 – 1 0 1 2 3 4 fi 4 8 14 18 20 14 10 6 6

If it is given that mean and variance are 59.5 and 413 respectively, determine actual class intervals.

Exercise 2.3 [Pages 33 - 34]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 2 Measures of Dispersion Exercise 2.3 [Pages 33 - 34]

Exercise 2.3 | Q 1 | Page 33

Mean and standard deviation of two distributions of 100 and 150 items are 50, 5 and 40, 6 respectively. Find the mean and standard deviations of all the 250 items taken together.

Exercise 2.3 | Q 2 | Page 33

For certain bivariate data, the following information is available.

 X Y Mean 13 17 S.D. 3 2 Size 10 10

Obtain the combined standard deviation.

Exercise 2.3 | Q 3 | Page 33

Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 2, 4, 6, 8, 10.
(Given: sqrt(3.6) = 1.8974)

Exercise 2.3 | Q 4 | Page 33

Find the coefficient of Variation of a sample which has mean equal to 25 and standard deviation of 5.

Exercise 2.3 | Q 5 | Page 33

A group of 65 students of class XI have their average height is 150.4 cm with coefficient of variation 2.5%. What is the standard deviation of their height?

Exercise 2.3 | Q 6. (i) | Page 33

Two workers on the same job show the following results:

 Worker P Worker Q Mean time for completing the job (hours) 33 21 Standard Deviation (hours) 9 7

Regarding the time required to complete the job, which worker is more consistent?

Exercise 2.3 | Q 6. (ii) | Page 33

Two workers on the same job show the following results:

 Worker P Worker Q Mean time for completing the job (hours) 33 21 Standard Deviation (hours) 9 7

Which worker seems to be faster in completing the job?

Exercise 2.3 | Q 7. (i) | Page 33

A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively. Which department has a larger bill?

Exercise 2.3 | Q 7. (ii) | Page 33

A company has two departments with 42 and 60 employees respectively. Their average weekly wages are Rs. 750 and Rs. 400. The standard deviations are 8 and 10 respectively. Which department has a larger variability in wages?

Exercise 2.3 | Q 8 | Page 33

The following table gives weights of the students of class A. Calculate the Coefficient of variation. ("Given": sqrt0.8 = 0.8944)

 Weight (in kg) Class A 25 – 35 8 35 – 45 4 45 – 55 8
Exercise 2.3 | Q 9 | Page 34

Compute coefficient of variation for team A and team B. ("Given": sqrt(26) = 5.099, sqrt(22) = 4.6904)

 No. of goals 0 1 2 3 4 No. of matches played by team A 18 7 5 16 14 No. of matches played by team B 14 16 5 18 17

Which team is more consistent?

Exercise 2.3 | Q 10 | Page 34

Given below is the information about marks obtained in Mathematics and Statistics by 100 students in a class. Which subject shows A the highest variability in marks?

 Mathematics Statistics Mean 20 25 S.D. 2 3
Miscellaneous Exercise 2 [Pages 35 - 36]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 2 Measures of Dispersion Miscellaneous Exercise 2 [Pages 35 - 36]

Miscellaneous Exercise 2 | Q 1 | Page 35

Find the range for the following data.
116, 124, 164, 150, 149, 114, 195, 128, 138, 203, 144

Miscellaneous Exercise 2 | Q 2 | Page 35

Given below the frequency distribution of weekly wages of 400 workers. Find the range.

 Weekly wages (in ’00 ₹) 10 15 20 25 30 35 40 No. of workers 45 63 102 55 74 36 25
Miscellaneous Exercise 2 | Q 3 | Page 35

Find the range for the following data:

 Classes 115 – 125 125 – 135 135 – 145 145 – 155 155 – 165 165 – 175 Frequency 1 4 6 1 3 5
Miscellaneous Exercise 2 | Q 4 | Page 35

The city traffic police issued challans for not observing the traffic rules:

 Day of the Week Mon Tue Wed Thus Fri Sat No. of Challans 40 24 36 58 62 80

Find Q.D.

Miscellaneous Exercise 2 | Q 5 | Page 35

Calculate Q.D. from the following data:

 X (less than) 10 20 30 40 50 60 70 Frequency 5 8 15 20 30 33 35
Miscellaneous Exercise 2 | Q 6 | Page 35

Calculate the appropriate measure of dispersion for the following data:

 Wages (In ₹) Less than 35 35 – 40 40 – 45 45 – 50 50 – 55 55 – 60 No. of workers 15 50 85 40 27 33
Miscellaneous Exercise 2 | Q 7 | Page 35

Calculate Q.D. of the following data:

 Height of plants (in feet) 2 – 4 4 – 6 6 – 8 8 – 10 10 – 12 14 – 14 14 – 16 No. of plants 15 20 25 12 18 13 17
Miscellaneous Exercise 2 | Q 8 | Page 35

Find variance and S.D. for the following set of numbers.
25, 21, 23, 29, 27, 22, 28, 23, 27, 25
(Given sqrt(6.6) = 2.57)

Miscellaneous Exercise 2 | Q 9 | Page 35

Following data gives no. of goals scored by a team in 90 matches:

 No. of goals scored 0 1 2 3 4 5 No. of matches 5 20 25 15 20 5

Compute the variance and standard deviation for the above data.

Miscellaneous Exercise 2 | Q 10 | Page 35

Compute arithmetic mean and S.D. and C.V.
(Given sqrt(296) = 17.20)

 C.I. 45 – 55 55 – 65 65 – 75 75 – 85 85 – 95 95 – 105 f 4 2 5 3 6 5
Miscellaneous Exercise 2 | Q 11 | Page 35

The mean and S.D. of 200 items are found to be 60 and 20 respectively. At the time of calculation, two items were wrongly taken as 3 and 67 instead of 13 and 17. Find the correct mean and variance.

Miscellaneous Exercise 2 | Q 12 | Page 35

The mean and S.D. of a group of 48 observations are 40 and 8 respectively. If two more observations 60 and 65 are added to the set, find the mean and S.D. of 50 items.

Miscellaneous Exercise 2 | Q 13 | Page 35

The mean height of 200 students is 65 inches. The mean heights of boys and girls are 70 inches and 62 inches respectively and the standard deviations are 8 and 10 respectively. Find the number of boys and combined S.D.

Miscellaneous Exercise 2 | Q 14 | Page 35

From the following data available for 5 pairs of observations of two variables x and y, obtain the combined S.D. for all 10 observations.
where, sum_("i" = 1)^"n" "x"_"i" = 30, sum_("i" = 1)^"n" "y"_"i" = 40, sum_("i" = 1)^"n" "x"_"i"^2 = 225, sum_("i" = 1)^"n" "y"_"i"^2 = 340

Miscellaneous Exercise 2 | Q 15 | Page 35

The mean and standard deviations of two brands of watches are given below:

 Brand-I Brand-II Mean 36 months 48 months S.D. 8 months 10 months

Calculate a coefficient of variation of the two brands and interpret the results.

Miscellaneous Exercise 2 | Q 16 | Page 36

Calculate coefficient of variation for the data given below [Given : sqrt(3.3) = 1.8166]

 C.I. 5 – 15 15 – 25 25 – 35 35 – 45 45 – 55 55 – 65 65 – 75 f 6 7 15 25 8 18 21

## Chapter 2: Measures of Dispersion

Exercise 2.1Exercise 2.2Exercise 2.3Miscellaneous Exercise 2

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 2 - Measures of Dispersion

Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 2 (Measures of Dispersion) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 2 Measures of Dispersion are Measures of Dispersion, Range of Data, Quartile Deviation (Semi - Inter Quartile Range), Variance and Standard Deviation, Standard Deviation for Combined Data, Coefficient of Variation.

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