Compare your answers.

The daily depth of the Milk River is shown for three months in 2012.

  1. Draw a histogram for each month using the same classes.

    Begin by drawing a frequency table for each month.

    DepthFrequency
      March June August
    0.4 - 0.5 5 0 0
    0.5 - 0.6 11 0 0
    0.6 - 0.7 7 0 0
    0.7 - 0.8 5 0 0
    0.8 - 0.9 2 6 31
    0.9 - 1.0 1 22 0
    1.0 - 1.1 0 2 0

    Use the frequency table to draw the histograms.



    1. Determine the range, mean, and standard deviation for each month.

       MarchJuneAugust
      Range 0.467 0.128 0.042
      Mean 0.623 0.933 0.830
      Standard
      Deviation      		 0.118 0.037 0.011




    2. Describe how the means and standard deviations are related to the histograms you drew in 1.

      The mean is near the center of the data represented in each histogram. March has the largest standard deviation. The histogram for March is the most spread out. August has the smallest standard deviation. The histogram for August is the least spread out.



    3. Suggest a relationship between the range and the standard deviation of a set of data.

      For this data, the month with the largest standard deviation also had the largest range and the month with the smallest standard deviation also had the smallest range. This makes sense because both a large range and a large standard deviation correspond to data that is "spread out". Having a large variation of river depths seems more reasonable during spring thawing than at the end of summer.

 

For further information about standard deviation see p. 254 of Principles of Mathematics 11.

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