Data Mining, 4th Edition

Thus the multistage decision property can be written in general as

$\mathrm{Entropy}(p,q,r)=\mathrm{entropy}(p,q+r)+(q+r)\cdot \mathrm{entropy}\left(\frac{q}{q+r},\frac{r}{q+r}\right)$

where $p+q+r=1$.

Because of the way the log function works, you can calculate the information measure without having to work out the individual fractions:

$\begin{array}{ll}\mathrm{Info}([2,3,4])\hfill & =-2/9\times \log 2/9-3/9\times \log 3/9-4/9\times \log 4/9\hfill \\ =[-2\log 2-3\log 3-4\log 4+9\log 9]/9.\hfill \end{array}$

This is the way that the information measure is usually calculated in practice. So the information ...