Data Distributions, Describing Variability and Comparing by Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N.

By Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, Elizabeth Difanis Phillips

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Again, the magnitude of the difference in measures when considered in the context of the problem, ordering a fitted cap, is negligible. 3 Variability in Numerical Measurements PACING 1 day Mathematical Goals • Recognize that variability occurs whenever data are collected • Use properties of distributions to describe the variability in a given data set • Use line plots to display data distributions • Decide if a difference among data values and/or summary measures matters Launch Ask students to explain what they think measurement data are and how these data might be collected.

The arrows indicate the distance each data value is from the mean. 2. 2 3. The two sums are equal. This reflects the A. 1. Possible answer: fact that the mean is a balance point. 4. It will always be true. 2 3 4 5 6 7 8 9 10 5. If you think of the distribution as a seesaw, Sugar per Serving (g) 1 2 3 4 5 6 7 8 9 10 Sugar per Serving (g) 2. Possible answers: a. 8 g and 9 g b. Range is greater for the second line plot. B. 1. a. Line plot: 1 2 3 4 5 6 7 8 9 10 11 12 Sugar per Serving (g) b. 6 g 2.

You will need to press the students to think about solutions that are more visual and that don’t rely on the algorithm. One way to make sure this happens is to ask these students to find a second solution that does not use the algorithm. This is important because, while they may be able to use the algorithm and recognize that it can be used in these situations, they may not have a firm conceptual understanding of the mean. qxd 3/13/06 5:47 PM Page 50 Summarize Share strategies for answering the questions.

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