Math

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For a set of scores, will the interquartile range always be
less than the range? Explain your answer with an example.

  • Math -

    Check this explanation of interquartile range.

    http://www.mathwords.com/i/interquartile_range.htm

    What do you think?

  • Math -

    Wow! This is hard!

    IQR=less than median - more than median
    Range= highest-lowest

    2 5 6 9 12

    Range=12-2=10
    median=6
    so
    IQR=10.5-3.5=7

    So I'm thinking yes?

  • Math -

    The interquartile range is the difference between the first and the third quartiles, and is always less than or equal to the range.
    In normally distributed data, it is less than the range.
    Example 1:
    48,60,65,80,85,92,99
    The quartiles are shown in bold, namely Q1=60, Q2=80, and Q3=92.
    The interquartile range is therefore 92-60=32.
    The range is 99-48=51

    Example 2:
    65,65,65,70,75,89,89
    The interquartile range is 89-65=24
    The range is also 89-65=24.
    This is an extreme example to illustrate that it is possible to have the interquartile range equal to the range, but highly unlikely in real life.

  • Math -

    Thanks for the help!

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