Question

The National Sporting Goods Association (NSGA) conducted a survey of the ages of people that purchased athletic footwear in 2009. The ages are summarized in the following relative frequency distribution. Assume the survey was based on 100 individuals.

Age of Purchaser | Percent |

Under 14 years old | 15 |

14 to 17 years old | 4 |

18 to 24 years old | 6 |

25 to 34 years old | 15 |

35 to 44 years old | 16 |

45 to 64 years old | 28 |

65 years old and over | 16 |

**
a.** Calculate the average age of this distribution. Use 10
as the midpoint of the first class and 75 as the midpoint of the
last class.

**
b.** Calculate the sample standard deviation.

Answer #1

Here we have the ages are summarized in the relative frequency distribution

We first find mid points of ages as

Age of Purchaser | Age mid point (m) | Percent (f) | m*f | m^2*f |

<14 | 10 | 15 | 150 | 1500 |

14 to 17 | 15.5 | 4 | 62 | 961 |

18 to 24 | 21 | 6 | 126 | 2646 |

25 to 34 | 29.5 | 15 | 442.5 | 13053.75 |

35 to 44 | 39.5 | 16 | 632 | 24964 |

45 to 64 | 54.5 | 28 | 1526 | 83167 |

>65 | 75 | 16 | 1200 | 90000 |

Total |
N=100 |
4138.5 |
216291.75 |

a) Average is

Thus Average age for this distribution is
**41.38**

**b**) Sample standard deviation is

first find variance

variance is,

Now Standard deviation is

Standard deviation is **21.32**

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14 to 17 years old
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35 to 44 years old
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