Topics
8. Statistics
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United States of America
Grade 6

Investigation: Find the best choice of center

Lesson
Practice
Overview
Activity 1
Activity 2
Reflection

Investigate which measure of center is the most representative for different data sets.

Objectives
  • To understand the difference between mean, median, and mode.
  • To determine which measure of center is the most representative of a data set.
  • To understand that measures of center can be misleading.
Materials
  • None

Finding the best choice of center - running times

Depending on the characteristics of the data, it may be better to use one measure of center 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.
The International Association of Athletics Federations recorded Usain Bolt's fastest times in the 100\text{ m} sprint for 7 years.

The results are recorded in the following table:

A table with title Usain Bolt's Fastest Annual Times 2007-2013. The table is consist of two columns titled Year and Time (seconds) and with 8 rows. Speak to your teacher for more information.

Find the mean, median, mode, and range for this data set.

Investigate
Consider the following questions once you have found the measures of center.
1.
In what year did Bolt record his fastest time?
2.
Find Usain Bolt's average time. What measure did you use, and why?

Finding the best choice of center - salaries

Ted is an employee who works for a company and currently gets paid \$26000 per year. He's decided to ask for his yearly pay rise to keep up with inflation.

Here is the breakdown of all the employees' salaries at the company he works for in a frequency table:

A table with two columns titled Annual Income and Number of Employees with 6 rows. Speak to your teacher for more information.

Find the mean, median, and mode for this data set.

Investigate
Consider the following questions once you have found the mean, median, and mode.
1.
What measure of center would the owner of the company use to describe the company's average annual income? Why?
2.
What measure of center would Ted use to describe the company's average annual income? Why?
3.
What measure of center would a mathematician who is not involved with the company use to describe the company's average annual income? Why?

Discuss your responses to the previous questions with a classmate, then answer the questions below.

Discussion
1.
Compare the measure of center that you used in the first activity with another classmate. Did you use the same measure or a different one? Discuss why you chose this measure.
2.
Knowing that different measures of center can prove a point, can you think of a time when you saw a misleading measure of center? If not, come up with an example of a misleading measure of center.

Outcomes

6.SP.B.5.D

Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered

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