#### Chapters

## Chapter 3: Skewness

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

For a distribution, mean = 100, mode = 127 and SD = 60. Find the Pearson coefficient of skewness Sk_{p}.

The mean and variance of the distribution is 60 and 100 respectively. Find the mode and the median of the distribution if Sk_{p} = – 0.3.

For a data set, sum of upper and lower quartiles is 100, difference between upper and lower quartiles is 40 and median is 30. Find the coefficient of skewness.

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.

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 |

Find Sk_{p} for the following set of observations.

17, 17, 21, 14, 15, 20, 19, 16, 13, 17, 18

Calculate Sk_{b} 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, 4.2, 3.5, 3.6, 5.2

For a frequency distribution Q_{3} – Q_{2} = 90 And Q_{2} – Q_{1} = 120, find Sk_{b}.

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

For a distribution, mean = 100, mode = 80 and S.D. = 20. Find Pearsonian coefficient of skewness Sk_{p}.

For a distribution, mean = 60, median = 75 and variance = 900. Find Pearsonian coefficient of skewness Sk_{p}.

For a distribution, Q_{1} = 25, Q_{2} = 35 and Q_{3} = 50. Find Bowley’s coefficient of skewness Sk_{b}.

For a distribution Q_{3} – Q_{2} = 40, Q_{2} – Q_{1} = 60. Find Bowley’s coefficient of skewness Sk_{b}.

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.

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.

Calculate Karl Pearsonian’s coefficient of skewness Sk_{p} 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 |

Calculate Bowley’s coefficient of skewness Sk_{b} 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 |

Find Sk_{p} for the following set of observations:

18, 27, 10, 25, 31, 13, 28.

Find Sk_{b} for the following set of observations:

18, 27, 10, 25, 31, 13, 28.

## Chapter 3: Skewness

## 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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