Question

Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of 744 households. Determine the class midpoint, if necessary, for each class and approximate the mean and standard deviation temperature

Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of 744 households. Determine the class midpoint, if necessary, for each class and approximate the mean and standard deviation temperature

Temp Frequency Class Midpoint

61-64 34 63

65-67 68 66.5

68-69 196 69

70 191 70.5

71-72 122 72

73-76 81 75

77-80 52 79

The sample standard deviation is _____degrees°F.

Answer #1

Frequency(f) | Midpoint(x) | fx | |

34 | 63 | 2142 | |

68 | 66.5 | 4522 | |

196 | 69 | 13524 | |

191 | 70.5 | 13465.5 | |

122 | 72 | 8784 | |

81 | 75 | 6075 | |

52 | 79 | 4108 | |

Total | 744 | 495 | 52620.5 |

Frequency(f) | Midpoint(x) | fx | (x-mu) | (x-mu)^2 | f*(x-mu)^2 | |

34 | 63 | 2142 | -7.73 | 59.69847 | 2029.748 | |

68 | 66.5 | 4522 | -4.23 | 17.86312 | 1214.692 | |

196 | 69 | 13524 | -1.73 | 2.980728 | 584.2227 | |

191 | 70.5 | 13465.5 | -0.23 | 0.051293 | 9.796869 | |

122 | 72 | 8784 | 1.27 | 1.621857 | 197.8666 | |

81 | 75 | 6075 | 4.27 | 18.26299 | 1479.302 | |

52 | 79 | 4108 | 8.27 | 68.45116 | 3559.46 | |

Total | 744 | 495 | 52620.5 | 9075.088 |

The sample standard deviation is **3.49**
degrees°F.

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