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2.22: Standard Deviation (3 of 4)

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    Learning Objectives

    • Next we summarize our observations with a focus on comparing the two groups:

      From this analysis, we can see that the group of students in the fifth and seventh grades are carrying more weight on average in their backpacks. The mean weight for this group is 14.2 pounds compared to 5.8 pounds for the group of first and third graders. There is also more variability in backpack weights in the fifth- seventh-grade group. The standard deviation for this group is 7.2 pounds, compared to 2.1 pounds for the younger students.

      One plausible explanation is that as children get older, they are assigned more homework, so they carry more in their backpacks. But at this age, we may also see more students making independent decisions about how much homework they will do, so some students will carry more books home and others will carry fewer.

    Learn By Doing

    Consider the following two quantitative data sets:

    Can two data sets have the same mean but different standard deviations? Can two data sets have different means but the same standard deviation? Use the simulation to investigate these questions in the next two activities.

    Instructions for adding or removing data points:

    This page titled 2.22: Standard Deviation (3 of 4) is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Bill Pelz via source content that was edited to the style and standards of the LibreTexts platform.