Each of 16 students measured the circumference of a tennis ball by four different methods, which were:

Method A: Estimate the circumference by eye.

Method B: Measure the diameter with a ruler, and then compute the circumference.

Method C: Measure the circumference with a ruler and string.

Method D: Measure the circumference by rolling the ball along a ruler.

The results (in cm) are as follows, in increasing order for each method:

Method A: 18.0, 18.0, 18.0, 20.0, 22.0, 22.0, 22.5,

23.0, 24.0, 24.0, 25.0, 25.0, 25.0, 25.0, 26.0, 26.4.

Method B: 18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4,

20.4, 20.4, 20.5, 21.2, 22.0, 22.0, 22.0, 22.0, 23.6.

Method C: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0,

21.0, 21.0, 21.0, 21.0, 21.5, 21.5, 21.5, 21.5, 21.6.

Method D: 20.0, 20.0, 20.0, 20.0, 20.2, 20.5, 20.5,

20.7, 20.7, 20.7, 21.0, 21.1, 21.5, 21.6, 22.1, 22.3.

a. Compute the mean measurement for each method.

b. Compute the median measurement for each method.

c. Compute the 20% trimmed mean measurement for each method.

d. Compute the first and third quartiles for each method.

e. Compute the standard deviation of the measurements for each method.

f. For which method is the standard deviation the largest? Why should one expect this method to have the largest standard deviation?

g. Other things being equal, is it better for a measurement method to have a smaller standard deviation or a larger standard deviation? Or doesn’t it matter? Explain.

Answer :

Step 1 of 7 :

Given a tennis ball by by four different method.

Each of 16 student measured.

Here n=16

Our goal is to find

a). Compute the mean measurement for each method.

b). Compute the median measurement for each method.

c). Compute 20% trimmed mean measurement for each method.

d). Compute the first and third quartile for each method.

e). The standard deviation of the measurement for each method.

f). For which method is the standard deviation the largest ?Why should one except this have

method to have the largest standard deviation.

g). Other things being equal,is it better for a measurement method to have a smaller standard deviation or a larger standard deviation ?or doesn’t it matter? Explain.

Step 1 of 7 :

a).

Now we have to compute the mean measurement for each method.

Method A :

18 |
24 |

18 |
24 |

18 |
25 |

20 |
25 |

22 |
25 |

22 |
25 |

22.5 |
26 |

23 |
26.4 |

Now we have to find the mean of method A.

Mean is the sum of the total numbers in the data set and divided by the total number.

Then the formula of the mean is

Therefore the method A mean is

Method B :

18.8 |
20.4 |

18.9 |
20.5 |

18.9 |
21.2 |

19.6 |
22 |

20.1 |
22 |

20.4 |
22 |

20.4 |
22 |

20.4 |
23.6 |

Now we have to find the mean of method B.

Mean is the sum of the total numbers in the data set and divided by the total number.

Then the formula of the mean is

Therefore the method B mean is

Method C :

20.2 |
21.0 |

20.5 |
21.0 |

20.5 |
21.0 |

20.7 |
21.5 |

20.8 |
21.5 |

20.9 |
21.5 |

21.0 |
21.5 |

21.0 |
21.6 |

Now we have to find the mean of method C.

Mean is the sum of the total numbers in the data set and divided by the total number.

Then the formula of the mean is

Therefore the method C mean is

Method D :

20 |
20.7 |

20 |
20.7 |

20 |
21 |

20 |
21.1 |

20.2 |
21.5 |

20.5 |
21.6 |