What’s Normal?

We’re about a third of the way in The Pit and the Pendulum unit and I think most of the cherubs are getting a nice understanding the importance of sample size, controlled experiments, and representing data with histograms. After our initial experiments with pendulums, they couldn’t agree if the weight of the bob really affected1 the period of the pendulum or not. I told them they needed a new tool to make that determination and so began our journey to the land of statistical significance.

We began been collecting data and collecting data. We’ve collected data on pulse rate, stride length, estimating 5 seconds, and average amount of time spent online. Making histogram after histogram. Making them on graph paper and on butcher block paper. Posting them around the classroom and comparing. We haven’t moved to creating them on the graphing calculator yet as I think they need experience doing it by hand first. Once I know that they know how to create and interpret a histogram, we’ll move to using the calculator. We’ve briefly talked about the normal curve and will delve deeper into measures of central tendency this week.

I’ve been using this site from Shodor to create histograms2. I like that we can quickly change the class width or add more data. Here is the pulse data for my first period:

Initially I was hoping for a more normal distribution. As it obviously didn’t work out that way, we combined the data from two classes3:

Still not quite normal. So we looked at the data with a class width of 4:

Better. In each class one student suggested that if we had even more data it would look more like a normal distribution when the class widths were one. Okay, they actually said something like “More like that curve it’s supposed to be” but I’ll take it.

1 I’ll admit right now, I’m going to goof up affect/effect repeatedly in this blog – let alone in this post. I’ve always had a mental block on this and I expect I always will.

2 I think this counts as a happy marriage of my digital projector and laptop, no?

3 Obviously 5th period had a little problem with either data collection or data recording as our n is not a multiple of ten.

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9 Responses to What’s Normal?

  1. Dan Meyer says:

    Yeah, that’s the stuff. Fun to see footnotes lying around here too.

  2. Mr. K says:

    I’m not sure whether the class width of 4 is “better”, but it does illustrate how much that choice can affect how you visually interpret the data.

    Part of the point of this exercise is to see how the data might not meet up with our expectations, no? The idea of massaging the presentation of a graph to “make it look like it’s supposed to” is a dangerous one, I think.

    (I realize that kids have trouble expressing themselves, and that ay not be what they meant. Still, it’s an opportunity to reinforce looking at data without preconceptions)

  3. Jackie says:

    Dan -Yep. I stole your footnote idea. Perhaps I should put in a footnote for the footnotes?

    Mr. K – Good point. I’ll reinforce the difference on Monday. Thanks.

  4. Mr. K says:

    I didn’t mean to come off as negative, btw – I think this is a great lesson.

    Part of my struggle with teaching statistics is that we have to practice on small data sets to understand the mechanisms by which they work, but those techniques don’t become meaningful until we get large enough amounts of data that it becomes unwieldy to do by hand.

    Your use of the histogram sites is a perfect transition between the two, i think. You can collect more data, and have the kids analyze the individual classes as well as the combined to see where that apparent bimodality comes from.

  5. Mr. K says:

    And, serendipitously, this just showed up in my rss feed – a real world example of how presentation can affect analysis, and why Disraeli said that thing about lies, damn lies, and statistics.

  6. Jackie says:

    Mr. K – No worries. I didn’t actually take your comment as negative. As for showing how more data will change things, Shodor has another nice applet which shows how increasing the number of trials changes things. I showed this to one class, I’ll be sure to bring it up again in both though.

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