Kelly’s coefficient of skewness for grouped data
For a symmetric distribution, the first decile namely $D_1$ and nineth decile $D_9$ are equidistance from the median i.e. $D_5$. Thus, $D_9 - D_5 = D_5 -D_1$.
Kelly’s coefficient of skewness is based on deciles $D_{1}$, $1^{st}$ decile, $D_{5}$, $5^{th}$ decile, and $D_{9}$, $9^{th}$ decile). Only 20% of the observations are excluded from the measure.
Formula
$Sk =\dfrac{D_9+D_1 -2*Median}{D_9-D_1}$
OR
$Sk =\dfrac{P_{90}+P_{10} -2*Median}{P_{90}-P_{10}}$
where,
$D_1 (=P_{10})$is the first decile (or tenth percentile) of the data$Median=D_5 (=P_{50})$is the median of the data$D_9 (=P_{90})$is the ninth decile (or nineteenth percentile) of the data.
