Question

Define and explain the following concept: Sheppard's Correction for the variance.

Answer 1

Sheppard's correction for variance, named after William Sheppard, are approximate adjustments to the calculated second-order sample moment for grouped data. When variance (2 moment) is calculated for continuous frequency distributions, there is an erroneous assumption that data is centered around the mid-points of class intervals and thus, creates grouping errors. The correction is as follows:

u2 = m2 - i2/12

where m2 is the measured second-order moment around te mean in the sample and i2/12 is the adjustment made to it where i is the class interval and u2 is corrected moment.