Sheppard’s Corrections for Moments in Statistics | Descriptive Statistics | Bsc Statistics

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The fundamental assumption that we make in farming class intervals is
that the frequencies are uniformly distributed about the mid points of
the class intervals. All the moment calculations in case of grouped
frequency distributions rely on this assumption. The aggregate of the
observations or their powers in a class is approximated by multiplying
the class mid point or its power by the corresponding class frequency.
For distributions that are either symmetrical or close to being
symmetrical, this assumption is acceptable. But it is not acceptable for
highly skewed distributions or when the class intervals exceed about
1/20th of the range. In such situations, W. F. Sheppard suggested some
corrections to be made to get rid of the so called “grouping errors” that
enter into the calculation of moments.

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