Question

Using the same data set as in 1, find the variance, standard deviation, and range, using the formulas. Using the same data set as in 1, find the variance, standard deviation, and range, using the formulas. Show the formulas and intermediate steps. Round your answers to the correct number of decimal places

data set 9, 2, 8, 2, -9, 5, 6, 2, -5, -9, 9, 4, 5, 5, -3, -1, 0

Answer #1

Solution:

Given data:

9, 2, 8, 2, -9, 5, 6, 2, -5, -9, 9, 4, 5, 5, -3, -1, 0

Creating table for calculation:

x | x2 |

9 | 81 |

2 | 4 |

8 | 64 |

2 | 4 |

-9 | 81 |

5 | 25 |

6 | 36 |

2 | 4 |

-5 | 25 |

-9 | 81 |

9 | 81 |

4 | 16 |

5 | 25 |

5 | 25 |

-3 | 9 |

-1 | 1 |

0 | 0 |

Sum=30 |
Sum=562 |

Formula of Sample variance:

Now, Sample standard deviation is

Range can be found using formula,

Range = Maximum value - minimum value

We need data in ascending order:

-9 |

-9 |

-5 |

-3 |

-1 |

0 |

2 |

2 |

2 |

4 |

5 |

5 |

5 |

6 |

8 |

9 |

9 |

Therefore, Range = 9 - (-9) = 18

Done

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Standard deviation (3 digits after decimal point):
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