###### Advertisements

###### Advertisements

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

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

###### Advertisements

#### Solution

The given data can be arranged in ascending order as follows:

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

Here, n = 7

∴ Q_{1} = value of `(("n" + 1)/4)^"th"` observation

= value of `((7 + 1)/4)^"th"` observation

= value of 2^{nd} observation

∴ Q_{1} = 13

Q_{2} = value of `2(("n" + 1)/4)^"th"` observation

= value of `2((7 + 1)/4)^"th"` observation

= value of (2 × 2)^{th} observation

= value of 4^{th} observation

∴ Q_{2} = 25

Q_{3} = value of `3(("n" + 1)/4)^"th"` observation

= value of `3((7 + 1)/4)^"th"` observation

= value of (3 × 2)^{th} observation

= value of 6^{th} observation

∴ Q_{3} = 28

Coefficient of skewness,

Sk_{b } = `("Q"_3 + "Q"_1 - 2"Q"_2)/("Q"_3 - "Q"_1)`

= `(28 + 13 - 2(25))/(28 - 13)`

= `(41 - 50)/15`

= `- 9/15`

∴ Sk_{b } = – 0.6

#### APPEARS IN

#### RELATED QUESTIONS

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.

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 |

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, 3.5, 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}.

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.

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 |