Middle School Statistics

How to Quantify Opinions

A recent twitter post by Math Coach Geoff (@emergentmath) from New York asked for help in quantifying a poster which lists pros and cons of using paper towels versus electric hand dryers.  The task reminded me of a quantitative data collection method I have used with Advanced Placement Statistics students.  After the AP exams in May, my students were required to develop and complete a project which demonstrated some application of what they had learned during the year, which were then presented at a Stats Fair at the beginning of June.

Without fail, a few groups would propose some sort of a taste test: cookies, ice cream, soda, coffee.  Ignoring the fact that taste tests always take 10 times longer to actually carry-out than students think, the inherent problem with taste tests is that the data you get isn’t all that exciting:  “we did a taste test….39 people liked Coke, 45 people liked Pepsi”…yawn….  We can do some hypothesis tests for proportions, maybe break it up by gender, and that’s about it.

Using number lines, and having volunteers record their opinions by placing a dot on the lines, allows for more interesting data.  Consider a test between two colas, Fizz and Shanta.  Make a 10cm number line for each, and let each end represent the extreme opinions:

Fizz 1

Invite volunteers to record their opinions by placing a mark anywhere on the number line:

Fizz 2

Then, measure the distance from the left side in centimeters.  The distance represent the taste score for each cola.

Fizz 3

Think about how much more rich the data is that we get from this method.  Not only do I have a record of which cola the volunteer prefers, but also a measure of the magnitude of the preference.  We could do a two-sample t-test of the means, do a one-sample test for the differences, and even look at a scatterplot of the score pairs.

We can use a similar approach to look at Geoff’s request.  In the pic he shared, the pros and cons of choosing between paper towels and electric hand dryers are listed:

Paper Towels

The electric dryer seems to have many more pros than paper towels, but just how compelling are these pros?  Perhaps one of the cons outweighs all of the pros?  How can we measure the magnitude of each of the arguments?  The number line method provide a means for us to quantify each of these items.  Create number lines from -10 to 10, attaching each to a statement from the poster.  Have students not only identify the pros and cons, but also judge how large or a pro or con each feature is by placing a dot on the number line.

Pros Cons

In a pre-algebra class, students can discuss how to combine all of the data points, and we have a natural “in” for wanting to add positive and negative integers.  “What’s the total con score?”, “What’s the total pro score?” and “What’s the overall score?”  Have students use the data and measurements they collect to defend their opinion, and use the natural opening to encourage writing in math class.


By Bob Lochel

HS Math Teacher. Hatboro-Horsham School District, Horsham, PA.

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