Problem 18BSC

In Exercise, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-2 where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Freshman 15 According to the “freshman 15” legend, college freshmen gain 15 pounds (or 6.8 kilograms) during their freshman year. Listed below are the amounts of weight change (in kilograms) for a simple random sample of freshmen included in a study (“Changes in Body Weight and Fat Mass of Men and Women in the First Year of College: A Study of the ‘Freshman 15”’ by Ffoffman, Policastro, Quick, and Lee,Journal of American College Health, Vol. 55, No. 1). Positive values correspond to students who gained weight and negative values correspond to students who lost weight. Is a weight gain of 15 pounds (or 6.8 kg)unusual? Why or why not? If 15 pounds (or 6.8 kg) is not unusual, does that support the legend of the “freshman 15”?

11 3 0 −2 3 −2 −2 5 −2 7 2 4 1 8 1 0 −5 2

Problem 18BSC

Answer:

Step1 of 3:

We have According to the “freshman 15” legend, college freshmen gain 15 pounds (or 6.8 kilograms) during their freshman year. Listed below are the amounts of weight change (in kilograms) for a simple random sample of freshmen included in a study (“Changes in Body Weight and Fat Mass of Men and Women in the First Year of College: A Study of the ‘Freshman 15”’ by Ffoffman, Policastro, Quick, and Lee,Journal of American College Health, Vol. 55, No. 1). Positive values correspond to students who gained weight and negative values correspond to students who lost weight. Is a weight gain of 15 pounds (or 6.8 kg)unusual? Why or why not? If 15 pounds (or 6.8 kg) is not unusual, does that support the legend of the “freshman 15”?

11 3 0 −2 3 −2 −2 5 −2 7 2 4 1 8 1 0 −5 2

Step2 of 3:

We need to find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-2 where we found measures of center. Here we find measures of variation.) Then answer the given questions.

Step3 of 3:

1).Range can be calculated by using the formula Range = maximum value - minimum value

The given data in Ascending order

-5 |
-2 |
-2 |
-2 |
-2 |
0 |
0 |
1 |
1 |
2 |
2 |
3 |
3 |
4 |
5 |
7 |
8 |
11 |

Here,

Maximum value = 11

Minimum value = -5

Now,

Range = maximum value - minimum value

= 11 - (-5)

= 11 + 5

= 15.

Therefore, Range = 15kg.

2).consider,

x |
||

-5 |
1.8888 |
47.45557 |

-2 |
1.8888 |
15.12277 |

-2 |
1.8888 |
15.12277 |

-2 |
1.8888 |
15.12277 |

-2 |
1.8888 |
15.12277 |

0 |
1.8888 |
3.567565 |

0 |
1.8888 |
3.567565 |

1 |
1.8888 |
0.789965 |

1 |
1.8888 |
0.789965 |

2 |
1.8888 |
0.012365 |

2 |
1.8888 |
0.012365 |

3 |
1.8888 |
1.234765 |

3 |
1.8888 |
1.234765 |

4 |
1.8888 |
4.457165 |

5 |
1.8888 |
9.679565 |

7 |
1.8888 |
26.12437 |

8 |
1.8888 |
37.34677 |

11 |
1.8888 |
83.01397 |

279.7778 |