## Statistics – My New Approach Continues

Today I covered discrete probability distributions in my statistics course. In the past, when discussing the mean and standard deviation of a probability distribution, I’d present the formulas and give a quick idea of what the mean and standard deviation represented. Looking back, I know my students most likely didn’t understand what they were doing, they just did it.

I’m trying to make things a little more conceptual this semester, with a focus on understanding. Here’s an example of my new approach.

I started by putting a table on the board for the probabilities of having 0, 1, 2, or 3 girls in a family with 3 children. One of students said “Mr. Woodbury, I never understand it when I read in the paper about the typical family having, like, 2.3 kids. What is that all about?” I could not have scripted it any better. I replied that no family has 2.3 children, but if we examined all families, the average number of children would be 2.3.

At this point I asked her, “If you took all the families with 3 children, how many girls would there be per family?” I brought up Microsoft Excel and typed “=RANDBETWEEN(0,1)” in cell A3, and copied the same expression to cells B3 & C3. I then copied these cells down to row 1002. “Do you know what I’ve done? I’ve simulated the genders of 3 children for 1000 families. The 0 represents that the child is a boy and a 1 represents that the child is a girl.” I typed “=SUM(A3:C3)” in cell D3 to accumulate the number of girls for each family. “See, the first family was BGB, so there is 1 girl. The second family was GGB, so there are 2 girls. And so on.”

To calculate the mean number of girls I typed “=AVERAGE(D3:D1002)” in cell D1. To calculate the standard deviation for the number of girls I typed “=STDEV(D3:d1002)” in cell D2. At this point they understood that the mean of a probability distribution was similar to the mean of a set of data, and that standard deviation was similar as well. They saw that the mean was close to 1.5, which made sense to them. By pressing the F9 key, I randomly generated 1000 families and again the mean was close to 1.5. I then started pressing the F9 key rapidly and noticed that the values danced all around 1.5. They also noticed that the standard deviations danced around 0.87.

When we went through the formulas they understood what we were trying to find, and they understood that the answers made sense.

Students are less likely to think that a subject is useless when you present the material in this fashion. Thinking is greater than mimicking. My students are more involved this semester, and seem to be doing much better as well.

I’d love to hear your comments. If there are activities or assignments that you are using to increase understanding or make connections, share them in the comment area, or send them to me through the contact page on my website – georgewoodbury.com .

-George

I am a mathematics instructor at College of the Sequoias in Visalia, CA. I blog about general teaching ideas every Wednesday. Let me know if there are other topics you’d like me to cover. You can email suggestions through the contact page on my website.