Which language is shortest?
R, 821 - 44 = 777 bytes

Updated results: please see the edit history to make sense of all the comments below.

           language num_answers avg_count median_count
1              RUBY          49  49.97959         30.0
2              CJAM          48  32.64583         22.0
3              PYTH          48  21.02083         14.0
4          PYTHON 2          46  86.78261         77.0
5             JULIA          43  58.90698         45.0
6           HASKELL          41  74.65854         56.0
7               PHP          40  73.52500         48.0
8              PERL          36  53.30556         34.0
9          PYTHON 3          34  90.91176         90.5
10       POWERSHELL          33  60.24242         44.0
11                C          32 221.84375         79.5
12                R          32  77.40625         62.5
13             JAVA          29 170.68966        158.0
14 JAVASCRIPT (ES6)          29  90.79310         83.0
15       JAVASCRIPT          28  68.39286         61.0
16               C#          25 193.92000        130.0
17      MATHEMATICA          23  56.04348         47.0
18           MATLAB          22  67.45455         55.0
19         TI-BASIC          19  47.05263         37.0
20              APL          18  16.55556         15.0


The code, which I could shorten a bit more:

W=library;W(XML);W(plyr)
X=xpathSApply;Y=xmlValue;D=data.frame;H=htmlParse;S=sprintf
Z="http://codegolf.stackexchange.com/"
R=function(FUN,...)do.call(rbind,Map(FUN,...))
G=function(url){d=H(url)
a=as.double(sub(".*?(\\d+)a.*","\\1",X(d,"//div[starts-with(@class,'status')]",Y)))
u=paste0(Z,X(d,"//*[contains(@class,'question-hyperlink')]",xmlGetAttr,"href"))
D(u,a)}
u=S("%s/questions/tagged/code-golf?page=%i",Z,1:50)
q=R(G,u)
u=with(q,head(u[a&gt;20],50))
A=function(url){u=S("%s?page=%i",url,1:10)
f=function(u){d=H(u)
h=X(d, "//div[@class='post-text']//h1",Y)
p="^(.*?),.*? (\\d+)( [Bb]ytes)?$"
k=grep(p,h,v=T)
l=toupper(sub(p,"\\1",k))
c=as.double(sub(p,"\\2",k))
D(l,c)}
R(f,u)}
a=R(A,u)
L=names(tail(sort(table(a$l)),20))
x=subset(a,l%in%L)
arrange(ddply(x, "l",summarise,n=length(c),a=mean(c),m=quantile(c,0.5)),-n)


De-golfed:

library(XML)
library(plyr)
LoopBind &lt;- function(FUN, ...) do.call(rbind, Map(FUN, ...))
GetQuestions &lt;- function(url) {
  d = htmlParse(url)
  a=as.double(sub(".*?(\\d+)a.*","\\1",xpathSApply(d, "//div[starts-with(@class, 'status')]", xmlValue)))
  u=paste0("http://codegolf.stackexchange.com/",xpathSApply(d, "//*[contains(@class, 'question-hyperlink')]", xmlGetAttr, "href"))
  data.frame(u, a)
}
u &lt;- sprintf("http://codegolf.stackexchange.com/questions/tagged/code-golf?page=%i", 1:50)
q &lt;- do.call(rbind, Map(GetQuestions, u))
u &lt;- with(q, head(u[a &gt; 20], 50))

GetAnswers &lt;- function(url) {
  u=sprintf("%s?page=%i",url,1:10)
  f=function(u) {
    d = htmlParse(u)
    h = xpathSApply(d, "//div[@class='post-text']//h1", xmlValue)
    p = "^(.*?),.*? (\\d+)( [Bb]ytes)?$"
    k = grep(p,h,v=T)
    l = toupper(sub(p,"\\1",k))
    c = as.double(sub(p,"\\2",k))
    data.frame(language=l,c)
  }
LoopBind(f,u)
}
a=LoopBind(GetAnswers, u)
L=names(tail(sort(table(a$l)),20))
x=subset(a,language%in%L)
arrange(ddply(x, "language", summarise, num_answers = length(c), avg_count = mean(c), median_count = quantile(c,0.5)),
        -num_answers)