A partial solution, but better than nothing:

#!/usr/bin/perl
$_=<DATA>;
$h{$_}++,$c++,$h{$_}>$n?($n=$h{$_},$m=$_):++$k for map {lc}m/\w+/g;
$_="$c words\nmax: '$m' ($n times)$\avg count:".($c/keys %h).$\;
print;BEGIN{$\=$/;$/=q//; $,=":"}
print@a while@a=each%h;

__DATA__
But, in a larger sense, we can not dedicate—we can not consecrate—-we 
+can not hallow—-this ground. The brave men, living and dead, who stru
+ggled here, have consecrated it, far above our poor power to add or d
+etract. The world will little note, nor long remember what we say her
+e, but it can never forget what they did here. It is for us the livin
+g, rather, to be dedicated here to the unfinished work which they who
+ fought here have thus far so nobly advanced. It is rather for us to 
+be here dedicated to the great task remaining before us — that from t
+hese honored dead we take increased devotion to that cause for which 
+they gave the last full measure of devotion — that we here highly res
+olve that these dead shall not have died in vain — that this nation, 
+under God, shall have a new birth of freedom — and that government of
+ the people, by the people, for the people, shall not perish from the
+ earth
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Update: now with average.