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High School — Mathematics
Data Analysis and Probability

Overview

Core Resources

    Data Analysis and Probability

    Strategies

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      Strategies: Advanced Work

      The following activities are suggestions for working with students who are ready for advanced work. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      The Standard Deviation

      This value tells us whether the data is spread over a large interval of values or whether it all fits in a small interval. Students who study this topic should understand how to compute the standard deviation for a small data set, and how to use a statistics package to compute the standard deviation for a large data set.


      Problem

      Based on the following data for two track teams, which team is more likely to have the first place runner in an upcoming 5 kilometer race?

      TeamMean Time on 5KStandard Deviation
      Hillside Hares18 minutes2 minutes
      Gainesville Greyhounds18 minutes5 minutes
      Method

      The two track teams have the same mean which means that the teams will probably perform similarly. However, the question asks us whether the winner will come from Hillside or Gainesville. We examine the standard deviations for an answer. Since the Hillside Hares have a standard deviation of 2 minutes, we can assume that their times are clustered around the mean of 18 minutes. The Greyhounds have a larger standard deviation which means that their runners' times are more spread out. This implies that the Greyhounds may have a runner that runs far faster than 18 minutes (and one that runs far slower). We cannot predict for sure, but we can make a valid guess that a member of the Greyhounds will win the race.

      Answer

      A member of the Gainesville Greyhounds will more likely win the race.

      Extension

      Have your students work in groups to design a survey and collect data from their peers. They should compute the standard deviation of their data. Then, they can compare their methodology and results with other groups.

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