Even More About Range

Like all measures of dispersion, the range of scores gets larger when the distribution of scores is more heterogeneous (dissimilar). The more homogeneous (similar) the scores, the smaller the range.

Range is easy to calculate. It is the highest score minus the lowest score. If the highest score is 11 and the lowest score is 3, the range equals 8. Range is the highest score minus the lowest score.

Naturally, if there is rounding involved, the range is from 11.49999 down to 2.50000. That is you would accept 11.4999 as still being 11 but 11.5000 would be considered a 12. And you would accept 2.5000 as being 3 but anything below that (2.4999 and lower) would be considered a 2. So some textbooks recommend adding 1 point to the range. According to this view, then, the range would be 11 minus 3 plus one; the range would equal 9.

For the purposes of our discussion, however, lets do it the easy way. Range is the high score minus the low score.

Although easy to calculate, range is not terribly helpful for describing the distribution. Without knowing what is being measured, a range of 12 is ambiguous. If we were measuring the number of points each basketball made during a game, a range of 12 would not be surprising. But if we were measuring the number of goals each hockey player made during a game, a range of 12 would be very unusual.

Range is a good way to check for input errors. If your were inputting scores from a 10-point quiz, a range of 72 would alert you to an input error. The maximum possible in a 10-point quiz is 10 and the lowest possible score is 0, the range should not be more than 10.

NOW YOU CHOOSE:
    Day 3: Dispersion
    A Bit More About Dispersion
    Even More About Dispersion
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    How To Calculate
        Range
        MAD
        Sum of Squares
        Variance
        Standard Deviation
    Formulas For Dispersion
    Practice Problems
    More Practice Problems
    Basic Facts About Dispersion
    Vocabulary
    Quiz 3
    Summary