Problem 9E

The Cambridge Power and Light Company selected a random sample of 20 residential customers. Following are the amounts, to the nearest dollar, the customers were charged for electrical service last month: (10%)

54 |
48 |
58 |
50 |
25 |
47 |
75 |
46 |
60 |
70 |

67 |
68 |
39 |
35 |
56 |
66 |
33 |
62 |
65 |
67 |

(a) compute the arithmetic mean and (b) indicate whether it is a statistic or a parameter.

Solution 9E

Step1 of 3:

From the given problem we have data set and it is given below:

54 |
48 |
58 |
50 |
25 |
47 |
75 |
46 |
60 |
70 |

67 |
68 |
39 |
35 |
56 |
66 |
33 |
62 |
65 |
67 |

Here our goal is:

a). We need to compute the arithmetic mean.

b). We need to indicate whether it is a statistic or a parameter.

Step2 of 3:

a).

The arithmetic mean of the given data is calculated by using the formula:

Consider,

S.No. |
X |

1 |
54 |

2 |
48 |

3 |
58 |

4 |
50 |

5 |
25 |

6 |
47 |

7 |
75 |

8 |
46 |

9 |
60 |

10 |
70 |

11 |
67 |

12 |
68 |

13 |
39 |

14 |
35 |

15 |
56 |

16 |
66 |

17 |
33 |

18 |
62 |

19 |
65 |

20 |
67 |

n = 20 |

Now,

Therefore, the arithmetic mean of the given data is $54.55.

Step3 of 3:

b).

A sample statistic, assuming that the power company serves more than 20 customers.