# Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 3 - Skewness [Latest edition]

## Solutions for Chapter 3: Skewness

Below listed, you can find solutions for Chapter 3 of Maharashtra State Board Balbharati for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board.

Exercise 3.1Miscellaneous Exercise 3
Exercise 3.1 [Page 43]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 3 Skewness Exercise 3.1 [Page 43]

Exercise 3.1 | Q 1 | Page 43

For a distribution, mean = 100, mode = 127 and SD = 60. Find the Pearson coefficient of skewness Skp.

Exercise 3.1 | Q 2 | Page 43

The mean and variance of the distribution is 60 and 100 respectively. Find the mode and the median of the distribution if Skp = – 0.3.

Exercise 3.1 | Q 3 | Page 43

For a data set, sum of upper and lower quartiles is 100, difference between upper and lower quartiles is 40 and median is 50. Find the coefficient of skewness.

Exercise 3.1 | Q 4 | Page 43

For a data set with upper quartile equal to 55 and median equal to 42. If the distribution is symmetric, find the value of lower quartile.

Exercise 3.1 | Q 5 | Page 43

Obtain the coefficient of skewness by formula and comment on nature of the distribution.

 Height in inches No. of females Less than 60 10 60 – 64 20 64 – 68 40 68 – 72 10 72 – 76 2
Exercise 3.1 | Q 6 | Page 43

Find Skp for the following set of observations.
17, 17, 21, 14, 15, 20, 19, 16, 13, 17, 18

Exercise 3.1 | Q 7 | Page 43

Calculate Skb for the following set of observations of yield of wheat in kg from 13 plots:

4.6, 3.5, 4.8, 5.1, 4.7, 5.5, 4.7, 3.6, 3.5, 4.2, 3.5, 3.6, 5.2

Exercise 3.1 | Q 8 | Page 43

For a frequency distribution Q3 – Q2 = 90 And Q2 – Q1 = 120, find Skb.

Miscellaneous Exercise 3 [Page 44]

### Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board Chapter 3 Skewness Miscellaneous Exercise 3 [Page 44]

Miscellaneous Exercise 3 | Q 1 | Page 44

For a distribution, mean = 100, mode = 80 and S.D. = 20. Find Pearsonian coefficient of skewness Skp.

Miscellaneous Exercise 3 | Q 2 | Page 44

For a distribution, mean = 60, median = 75 and variance = 900. Find Pearsonian coefficient of skewness Skp.

Miscellaneous Exercise 3 | Q 3 | Page 44

For a distribution, Q1 = 25, Q2 = 35 and Q3 = 50. Find Bowley’s coefficient of skewness Skb.

Miscellaneous Exercise 3 | Q 4 | Page 44

For a distribution Q3 – Q2 = 40, Q2 – Q1 = 60. Find Bowley’s coefficient of skewness Skb.

Miscellaneous Exercise 3 | Q 5 | Page 44

For a distribution, Bowley’s coefficient of skewness is 0.6. The sum of upper and lower quartiles is 100 and median is 38. Find the upper and lower quartiles.

Miscellaneous Exercise 3 | Q 6 | Page 44

For a frequency distribution, the mean is 200, the coefficient of variation is 8% and Karl Pearsonian’s coefficient of skewness is 0.3. Find the mode and median of the distribution.

Miscellaneous Exercise 3 | Q 7 | Page 44

Calculate Karl Pearsonian’s coefficient of skewness Skp from the following data:

 Marks above 0 10 20 30 40 50 60 70 80 No. of students 120 115 108 98 85 60 18 5 0
Miscellaneous Exercise 3 | Q 8 | Page 44

Calculate Bowley’s coefficient of skewness Skb from the following data:

 Marks above 0 10 20 30 40 50 60 70 80 No. of students 120 115 108 98 85 60 18 5 0
Miscellaneous Exercise 3 | Q 9 | Page 44

Find Skp for the following set of observations:
18, 27, 10, 25, 31, 13, 28.

Miscellaneous Exercise 3 | Q 10 | Page 44

Find Skb for the following set of observations:
18, 27, 10, 25, 31, 13, 28.

## Solutions for Chapter 3: Skewness

Exercise 3.1Miscellaneous Exercise 3

## Balbharati solutions for Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 3 - Skewness

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Concepts covered in Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board chapter 3 Skewness are Skewness, Asymmetric Distribution (Positive Skewness), Asymmetric (Negative Skewness), Measures of Skewness, Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness), Features of Pearsonian Coefficient, Bowley’s Coefficient of Skewness.

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