What is the c means in Charlier's Correction in computing moment?

Question

On my book of Statistics it says the Sheppard's Correction in computing moment is :

Corrected $m_2=m_2-c^2/12$

Can someone tell me what is c in this formula?

Answer 1

You can find a description on Wikipedia

Sheppard's corrections are applied to correct estimates of moments computed from binned normally distributed data

$c$ is the bin width or class interval.

I would expect the binning would often expand the apparent dispersion of the distribution (ignoring the pathological case of a single bin) and the correction attempts to take this into account.

The correction is perhaps related to the fact that the variance of a continuous uniform distribution on the interval $[a,b]$ is $\dfrac{(b-a)^2}{12}$, i.e. when the width is $c=b-a$ then the variance is $\dfrac{c^2}{12}$.