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The Best Spread

Module by: Interactive Mathematics Program

Intent

Students revisit their work on Data Spread, using the new tool of standard deviation. Their work will offer a sense of how comfortable they are with both standard deviation and the general idea of data spread.

Mathematics

Standard deviation is the most widely used statistic for measuring the spread of a data set. In this activity, students will revisit data for which they have already tried several other measures of spread, using standard deviation. Question 4 highlights the idea that different measures of spread can give different pictures of a distribution. For example, the data set 4, 4, 7, 9, 9 has a range of 5 and a standard deviation of about 2.24, while the set 3, 7, 7, 7, 10 has a greater range of 7 but a smaller standard deviation of about 2.23.

Progression

Students work together to solidify their ability to calculate standard deviation, work individually on the other questions, and then share their results in a class discussion.

Approximate Time

10 minutes for introduction

15 minutes for activity (at home or in class)

15 minutes for discussion

Classroom Organization

Whole class, then individuals, followed by whole-class discussion

Materials

Students’ work on Data Spread

Doing the Activity

Have students work together to compute the standard deviation for one set of data before they work on their own.

Discussing and Debriefing the Activity

You might have students check their calculations for Question 2 in their groups. If there is disagreement, have volunteers present the calculations for the four sets of data. Then decide whether discussion of Question 3 seems needed.

A discussion of Question 4 is also optional. If you want to give students a hint for how to approach the problem, suggest they start with a particular data set and look for ways to change it

  • first, so that the range stays the same but the standard deviation gets smaller, and
  • second, so that the standard deviation stays the same (or at least stays smaller than that for the original set) but the range increases.

Make sure everyone understands how to calculate standard deviation.

Wrap up this activity by returning to the reference material Standard Deviation Basics and discussing the geometric interpretation of standard deviation. Students first encountered the ideas presented here in their work on An (AB)Normal Rug, so you might ask them to review their work on that activity before discussing the material in the reference pages.

Supplemental Activity

Data for Kai and Mai (reinforcement) poses questions similar to Question 4 of The Best Spread.

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