Transforming Data (Lesson 2.2)
Chapter 2  Day 2
Learning Targets

Describe the effect of adding or subtracting a constant on a distribution of quantitative data.

Describe the effect of multiplying or dividing by a constant on a distribution of quantitative data.

Analyze the effect of adding or subtracting a constant and multiplying or dividing by a constant on measures of center, location, and variability.
Experience First
This Activity uses the same context as in the previous lesson: Chapter 1 Test scores. In this lesson, students will investigate what happens to the distribution of scores when Mr. Wilcox applies a “curve” to the original test scores.
Students will need time to construct each of the dotplots, but this time is well spent. Once they have the visual of the dotplots, it is very easy to see what happens to shape, center, and variability. No calculations are necessary for this analysis, but students that want to calculate measures of center and variability will arrive at the same conclusion.
When asking students about shape, ask them “Is the shape exactly the same?” (yes it is!). For helping them to understand what happens to center and variability, encourage them towards analyzing the dotplot rather than calculations of mean, standard deviation, etc.
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Formalize Later
Stress to students that adding or subtracting a constant is just a “shift” of the data. When the data shifts to the left or right, the shape does not change, while the center does shift to the left or right. For variability, many students will want to say that it increases by 5, but challenge them to look at the visual of the dotplot or even to calculate the range before and after the 5point curve.
Stress to students that multiplying or dividing by a constant is just an “expansion” or “contraction” of the data. This expansion/contraction does not change the shape but does expand/contract the center. For variability, some students will look at the two dotplots and decide they are “spread out exactly the same”. Remind these students to look at the scale on the axis or even to calculate the range before and after the double the score curve.