Compare prediction rates between K means clustering and Multinomial Regression

May 2010
Stat/Math wizs, if you could kindly shine your beacon on this problem.

I'm running some statistics using a k means clustering algorithm and it had classified objects in category A, 33 in Cat B, 41 into Cat C and 24 into Cat D.

Out of a total of 144 objects, Cat A then has a proportion of 32% (0.319), 22.9%, 28.4%, and 16.6% respectively.

I was given a formula by a professor which involves the follow calculation

1. Squaring each proportion and then adding them to get the sum (0.319^2 + 0.229^2 ....)
2. This yielded a value of 0.263
3. Multiply 0.263 by 1.25 to get 0.329

The professor then said, within the context of a multinomial regression which yielded a prediction rate of 53%, that this particular set of classification results reflects a prediction rate of 32.9%. I didnt get a chance to clarify what he meant and, more importantly what formula he was applying. Could anyone shed light on what statistical formula was used to derive the value of 0.329 or 33%?

Thanks guys