Sum

A teacher asked the students to complete 60 pages of a record notebook. Eight students have completed only 32, 35, 37, 30, 33, 36, 35 and 37 pages. Find the standard deviation of the pages yet to be completed by them.

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#### Solution

The remaining number of pages to be completed is 60 – 32, 60 – 35, 60 – 37, 60 – 30, 60 – 33, 60 – 36, 60 – 35 and 60 – 37

The pages to be completed are, 28, 25, 23, 30, 27, 24, 25, and 23

Arrange in ascending order we get, 23, 23, 24, 25, 25, 27, 28 and 30

x_{i} |
x_{i}^{2} |

23 | 529 |

23 | 529 |

24 | 576 |

25 | 625 |

25 | 625 |

27 | 729 |

28 | 784 |

30 | 900 |

`sumx_"i"` = 205 |
`sumx_"i"^2` = 5297 |

Here n = 8, `sumx_"i"` = 205, `sumx_"i"^2` = 5297

Standard deviation (σ) = `sqrt((sumx_"i"^2)/"n" - ((sumx_"i")/"n")^2`

= `sqrt(5297/8 - (205/8)^2`

= `sqrt(662.13 - 42025/64)`

= `sqrt(662.13 - 656.64)`

= `sqrt(5.49)`

= 2.34

Standard deviation (σ) = 2.34

Concept: Measures of Dispersion

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