Giving a Useful Context for Standard Deviation

Wow, it’s been a month since school started. Evidently, I’ve been busier than I realized…but it’s time to get back into regularly reflecting on my teaching.

Over the summer, I saw an interesting statistics task as an introduction to variability:

Rank the following from most fair to least fair:
1.2 Variance and Standard Deviation_2

My students’ prior knowledge only consisted of how to calculate the mean. I gave this task in order to introduce variability and create a need for a numerical measurement of how spread out values are.

After giving my students three minutes with a partner, here’s how everything sorted out:
1.2 Variance and Standard Deviation_3

I asked the group how they defined “fair” in this task (since I never defined it for them). They decided that the more uniform that the distribution is, the more fair.

The entire class agreed on allocation A being the most fair, allocation D being the next most fair, and allocation B being the least fair. The real problem came with ranking the order of allocations C and E. I opened the floor for debate and there were good arguments for both allocations. My students then turned to me for help. They wanted a way to settle the argument. So, we discussed standard deviation:

1.2 Variance and Standard Deviation_4

…and we practiced calculating…

1.2 Variance and Standard Deviation_5

My students then went back and calculated the standard deviation for each of the allocations and re-ranked them:

1.2 Variance and Standard Deviation_3

My hope was to create a need for standard deviation. My students decided that standard deviation is a measure of how spread out data is from the mean. They also concluded that the larger the standard deviation is, the more spread out the values are. This task lead to a great 45+ minute statistical conversation…hopefully, I can find some more good tasks for future concepts.

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