Descriptive Statistics
How Difficult is it to Make a Pie Chart?

Reality Check
Year One
This is a pie chart that was included with a United Way payroll donation drive.  At first glance it appears that for every dollar donated, 29 cents goes to "Nurturing Children and Youth" program, 20 cents goes to "Developing Self-Sufficiency" programs, etc.  

 However, upon closer inspection, the United Way pie chart is inaccurate.  The sum of the percentages within the pie chart is 100%, thus accounting for every cent of a dollar.  However, the caption outside of the pie chart states that the "Administrative Cost" is 12.8%.  This makes the sum of the United Way expenses 112.8%, not 100%.  In reality, $0.128 of every dollar donated goes toward administrative costs.

I wrote the United Way about their incorrect graph, but they never responded.  

Year Two
I wrote them about their misleading pie chart.  There was no response.  I know I was not the only person writing them and they did change their pie chart the following year. 

This pie chart is also inaccurate.  Once again the slices sum to 100%.  Rather than list the administrative cost off to the side of the pie chart as they did the previous year, a statement stating that more that 87 cents of every dollar goes toward supporting agencies.

Year Three
Another year, another letter with the same result, no response from the United Way.  The following year United Way found a way to avoid the problem. They dropped the pie chart.  They just listed the programs they supported.

As a class activity, we correct the United Way graph and look at ways to display the data.

Distribution

Relative Frequency

Degrees

  Administrative Costs

0.128

0.128(360) 46

  Nurturing Children

0.29(0.872) 0.253

0.253(360) 91

  Develop Self-Sufficiency

0.20(0.872) 0.174

0.174(360) 63

  Health & Wellness

0.16(0.872) 0.140

0.140(360) 50

  Strengthen Families

0.22(0.872) 0.192

0.192(360) 69

  Strong Communities

0.13(0.872) 0.113

0.113(360) 41

  Totals

1.0000

360

A. Pie Chart

B.  Horizontal Frequency Bar Graph

Students have difficulty with Horizontal and Vertical.  They also have difficulty with labels.  Many students will label the x axis as cents.  This is incorrect.  0.15 cents equals $0.0015.

A source for graphs, both good and bad is USA Today.  They have graphs everyday.   Some graphs follow the rules for graphs covered in this chapter and other graphs are incorrectly drawn.

 "Average" is an Ambiguous Term
There is more than one statistic that can be called an average.  A person may think that one type of
"average" is being used when the other "average" is actually being used.  Mean and Median are the two
"averages" studied in this chapter. Listen to the Public Broadcasting Radio segment on this subject.

Click on the "Radio" on the left.  It will play a soundtrack about the ambiguous term "average", "The Median vs. the Mean in the Age of Average", by Mike Pesca .  This selection was originally aired on National Public Radio (NPR).  When you are linked to the page, select "LISTEN" to play  the interview.

 

Click on the hand   to go to the project.