Statistics

UK Secondary (7-11)

Where is the centre? (Investigation)

Lesson

In Measuring your Data, we looked at how the shape of the data affects measures of centre and spread. Depending on the characteristics of the data, it may be better to use one measure over another. A person's choice of measure may also be affected by the point they want to make.

Ted works for a company and he wants a pay raise. Here is the breakdown of the employees' salaries:

Annual Income | Number of Employees |
---|---|

$\$400000$$400000 | $1$1 |

$\$150000$$150000 | $3$3 |

$\$62000$$62000 | $5$5 |

$\$58000$$58000 | $10$10 |

$\$26000$$26000 | $4$4 |

- Find the mean, median and mode for this data set.
- What measure of central tendency would the owner of the company use to describe the company's average annual income? Why?
- What measure of central tendency would Ted use to describe the company's average annual income? Why?
- What measure of central tendency would a statistician use to describe the company's average annual income? Why?

The *International Association of Athletics Federations* recorded Usain Bolt's fastest times in the $100$100m sprint in each of the last $7$7 years. The results are recorded in the table below:

Usain Bolt's Fastest Annual Times 2007-2013 | |
---|---|

Year | Time (seconds) |

$2013$2013 | $9.77$9.77 |

$2012$2012 | $9.63$9.63 |

$2011$2011 | $9.76$9.76 |

$2010$2010 | $9.82$9.82 |

$2009$2009 | $9.58$9.58 |

$2008$2008 | $9.69$9.69 |

$2007$2007 | $10.03$10.03 |

- In what year did Bolt record his fastest time?
- Find the range of Bolt's times over the seven year period.
- Find Usain Bolt's average time. What measure did you use, and why?
- Plot this data in a column graph. Describe the centre and spread of this data.

Mr Brown is the CEO of a very successful company. As a rule, Mr Brown assigns two people to each task, promotes the one who does better, and fires the one who does worse. He picks two employees to analyse the data- Susan and Sean. Susan reports that the IQR is 30. Sean reports that the MAD is 16. "How can that be?!" shouts Mr Brown, "One of your estimates if almost double the other." Susan and Sean insist that they are both correct. Explain.