## 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.