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Investigation: Finding the best choice of center

Lesson

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. With the mean, median and mode to choose from, we could use the one which best proves our desired point.

 

Activity 1

Ted is an employee works for a company and currently only gets paid $\$26000$$26000 per year, so he wants a pay raise. Here is the breakdown of the employees' salaries as both a list and in a frequency table:

$\$26000,\$26000,\$26000,\$26000,\$58000,\$58000,\$58000,\$58000,\$58000,\$58000,\$58000,\$58000,\$58000,\$58000,\$62000,\$62000,\$62000,\$62000,\$62000,\$150000,\$150000,\$150000,\$400000$$26000,$26000,$26000,$26000,$58000,$58000,$58000,$58000,$58000,$58000,$58000,$58000,$58000,$58000,$62000,$62000,$62000,$62000,$62000,$150000,$150000,$150000,$400000

Annual Income Number of Employees
$\$26000$$26000 $4$4
$\$58000$$58000 $10$10
$\$62000$$62000 $5$5
$\$150000$$150000 $3$3
$\$400000$$400000 $1$1

Discussion questions

  1. Find the mean, median and mode for this data set.
  2. What measure of central tendency would the owner of the company use to describe the company's average annual income? Why?
  3. What measure of central tendency would Ted use to describe the company's average annual income? Why?
  4. What measure of central tendency would a mathematician who is not involved with the company use to describe the company's average annual income? Why?

 

Activity 2

The International Association of Athletics Federations recorded Usain Bolt's fastest times in the $100$100 m sprint for $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

Discussion questions 

  1. In what year did Bolt record his fastest time?
  2. Find the range of Bolt's times over the seven-year period.
  3. Find Usain Bolt's average time. What measure did you use, and why? 

 

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