Question

Calculate the sample mean and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants. If necessary, round to one more decimal place than the largest number of decimal places given in the data.

Class | Frequency |
---|---|

8.76-10.5 | 32 |

10.51-12.25 | 25 |

12.26-14 | 44 |

14.01-15.75 | 16 |

15.76-17.5 | 16 |

Answer #1

Here we have frequency distribution of hourly wages for a sample of pharmacy assistants as,

Hourly Wages (in dollars) | |

Class |
Frequency |

8.76-10.5 |
32 |

10.51-12.25 |
25 |

12.26-14 |
44 |

14.01-15.75 |
16 |

15.76-17.5 |
16 |

we have to find sample mean and sample variance

Class |
Mid Point m |
Frequency f |
m*f | m^2 * f |

8.76-10.5 |
9.63 | 32 | 308.16 | 2967.5808 |

10.51-12.25 |
11.38 | 25 | 284.5 | 3237.61 |

12.26-14 |
13.13 | 44 | 577.72 | 7585.4636 |

14.01-15.75 |
14.88 | 16 | 238.08 | 3542.6304 |

15.76-17.5 |
16.63 | 16 | 266.08 | 4424.9104 |

Total |
133 |
1674.54 |
21758.195 |

Sample mean is ,

Hence Sample mean = **12.59**

Now we find sample variance

Where

Thus sample variance is **5.11**

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120.9 - 124.6
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41 - 5241 - 52
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53 - 6453 - 64
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89 - 10089 - 100
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3
67 - 72
12
73 -78
8
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9
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Class
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61 - 66
13
67 - 72
9
73 - 78
5
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3
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