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![Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board chapter 2 - Measures of Dispersion - Shaalaa.com](/images/mathematics-and-statistics-2-commerce-english-11-standard-maharashtra-state-board_6:9684612829e8479ba15a6f1116dd16f2.jpg "Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board chapter 2 - Measures of Dispersion")
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Solutions for Chapter 2: Measures of Dispersion
Below listed, you can find solutions for Chapter 2 of Maharashtra State Board Balbharati for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board.
Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board 2 Measures of Dispersion Exercise 2.1 [Pages 26 - 27]
Find range of the following data:
575, 609, 335, 280, 729, 544, 852, 427, 967, 250
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 |
Find range of the following data.
| Classes | 62 – 64 | 64 – 66 | 66 – 68 | 68 – 70 | 70 – 72 |
| Frequency | 5 | 3 | 4 | 5 | 3 |
Find the Q.D. for the following data.
3, 16, 8, 15, 19, 11, 5, 17, 9, 5, 3.
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
Calculate Q. D. for the following data:
| X | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| F | 6 | 5 | 3 | 2 | 4 | 7 | 3 |
Following data gives the age distribution of 240 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 |
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 |
Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board 2 Measures of Dispersion Exercise 2.2 [Pages 30 - 31]
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
Find the various and S.D. for the following set of numbers.
65, 77, 81, 98, 100, 80, 129
Compute variance and standard deviation for the following data:
| x | 2 | 4 | 6 | 8 | 10 |
| f | 5 | 4 | 3 | 2 | 1 |
Compute the variance and S.D.
| x | 1 | 3 | 5 | 7 | 9 |
| Frequency | 5 | 10 | 20 | 10 | 5 |
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 |
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.
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 |
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.
Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board 2 Measures of Dispersion Exercise 2.3 [Pages 33 - 34]
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.
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.
Calculate coefficient of variation of marks secured by a student in the exam, where the marks are: 2, 4, 6, 8, 10.
(Given: `sqrt8` = 2.8284)
Find the coefficient of Variation of a sample which has mean equal to 25 and standard deviation of 5.
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?
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?
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?
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?
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?
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 |
Compute coefficient of variation for team A and team B.
| No. of goals | 0 | 1 | 2 | 3 | 4 |
| No. of matches played by team A | 19 | 6 | 5 | 16 | 14 |
| No. of matches played by team B | 16 | 16 | 5 | 18 | 15 |
Which team is more consistent?
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 |
Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board 2 Measures of Dispersion Miscellaneous Exercise 2 [Pages 35 - 36]
Find the range for the following data.
116, 124, 164, 150, 149, 114, 195, 128, 138, 203, 144
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 |
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 |
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.
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 |
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 |
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 |
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)
Following data gives no. of goals scored by a team in 100 matches:
| No. of goals scored | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of matches | 15 | 20 | 25 | 15 | 20 | 5 |
Compute the variance and standard deviation for the above data.
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 |
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.
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.
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.
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
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.
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 |
Solutions for 2: Measures of Dispersion
Balbharati solutions for Mathematics and Statistics 2 (Commerce) [English] 11 Standard Maharashtra State Board chapter 2 - Measures of Dispersion
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Concepts covered in Mathematics and Statistics 2 (Commerce) [English] 11 Standard 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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