Draft high school Statistics and Probability progression

Here is the progression on high school Statistics and Probability. As usual, comments welcome, and make sure you are using an up-to-date pdf reader.

[30 July 2012] This thread is now closed. Please go here to discuss this progression.

About Bill McCallum

I was born in Australia and came to the United States to pursue a Ph. D. in mathematics at Harvard University, met my wife, and never went back. I am a professor at the University of Arizona, working in number theory and mathematics education.
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12 Responses to Draft high school Statistics and Probability progression

  1. Philip Ogbuehi says:

    This document will be very helpful as my District embarks on the common core journey. I am wondering whether you have a similar document for HS Algebra and Geometry.

  2. CK says:

    These documents are in the works (I’m the editor).

  3. Howard Levine says:

    It seems that we want students to learn about margin of error by simulating a large number of samples based on certain assumed characteristics (parameters) of a population. Sample means or proportions will be graphed in dot plots or histograms. A smooth curve will be roughly fitted to the plot, and the inflection points will be used to estimate the standard deviation of the sample statistic. The sampling error will be considered to be equal to 2 standard deviations of the sample statistic. Is this how you see it?

  4. You are right that simulation is called for, but I’m not sure about the method you propose. First, I think the standard deviation would be estimated from the numerical data (e.g. the square root of the mean square distance from the mean, possibility built into statistical software). Second, two standard deviations is only the margin of error at the 95% confidence level (approximately); choosing a different level would change the margin.

    • Howard Levine says:

      If we can use the standard deviation of the sample, why can’t we use the Central Limt Theorem and traditional hypothesis testing? Why must we simulate sampling distributions? Why is one procedure or technology better than the other? The Guidelines for Assessmant and Instruction in Statistics Education (GAISE) Report cites several times that simulation will be used, but in an example they discuss (page 77) they talk about doing a certain simulation 200 times before being able to make a decision. This just is not possible to do in a timely fashion if more than one example is ever going to be done.

  5. The Central Limit Theorem is beyond the scope of the standards. The value of simulation is that it shows the theorem in action. Students who have some experience with simulation may be in a position to better understand the theorem when they encounter it later. Also, the simulations can be run by technology. So, running 200 simulations could be as simple as dragging a row in Excel down 200 times, or evn more automated than that.

  6. Hello– When I download, I don’t get any graphics until the end. Is anyone else having this problem? The text is still very informative and valuable, but I would deeply appreciate the illustrations!

  7. qsareweirdos says:

    At the end of paragraph 2: “Students should see that the standard deviation is the appropriate measure of spread for data distributions that are approximately normal in shape, as the standard deviation then has a clear interpretation related to relative frequency.”

    Can’t you get a clear interpretation of relative frequency from (nearly) any measure of spread and any known distribution? For example, with a uniform distribution, you can tell the fraction of the cases that are within 1 standard deviation of the mean. With a normal distribution, you can tell the fraction of cases that are within 1 MAD of the mean.
    qsareweirdos = Ken

    • Bill McCallum says:

      Good point. I guess maybe it should “as the standard deviation then has a well-known interpretation …”

  8. ingristro says:

    Regarding S-ID.4, how do you see students “fitting” data to a normal distribution at this level?

    • Bill McCallum says:

      They could either use technology or they could just use the expression for the normal distribution in terms of these parameters. Also, I think it would be better if the standard had said “fit a normal distribution to the data” not the other way around.

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