In Exercises, find the range, variance, and standard deviation for the given samph 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.

Saints in Super Bowl

Listed below are the numbers on the jerseys of the starting lineup for the New Orleans Saints when they recently won their first Super Bowl football game. What do the measures of variation tell us about the team? Does it make sense to compute the measures of variation for these data?

Problem 19BSC

Answer:

Step1 of 3:

We have Listed below are the numbers on the jerseys of the starting lineup for the New Orleans Saints when they recently won their first Super Bowl football game.

x | 9 | 23 | 25 | 88 | 12 | 19 | 74 | 77 | 76 | 73 | 78 |

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

9 | 12 | 19 | 23 | 25 | 73 | 74 | 76 | 77 | 78 | 88 |

Here,

Maximum value = 88

Minimum value = 9

Now,

Range = maximum value - minimum value

= 88 - 9

= 79

Therefore, Range = 79.

2).consider,

...x | (x -)2 | |

9 | 50.3636 | 1710.947 |

12 | 50.3636 | 1471.766 |

19 | 50.3636 | 983.6754 |

23 | 50.3636 | 748.7666 |

25 | 50.3636 | 643.3122 |

73 | 50.3636 | 512.4066 |

74 | 50.3636 | 558.6794 |

76 | 50.3636 | 657.225 |

77 | 50.3636 | 709.4978 |

78 | 50.3636 | 763.7706 |