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Perl, ok?
perl -lane 'print "$F[0] ", int(rand($F[2]-$F[1])) + $F[1]' file

Hope this could help you,

awk 'NR%4==2{sub("T*|A*","");l=length($0)}NR%4==0{$0=substr($0,length($0)-l+1)}1' file

As the file is already sorted you can do it in 1 pass:

awk 'function p(){for(I=C;I;I--)print R" "T/C} $1!=R{C=T=p()} {R=$1;C++;T+=$2} END{p()}' infile

awk 'NR==FNR{A[$1]++;B[$1]+=$2;next}{$2=B[$1]/A[$1]}1' infile infile

Try this,

awk '{if(! a[$1]) {a[$1]=$2;j=0;b[$1]=++j}else{a[$1]=a[$1]+$2;b[$1]=++j}} END{for (i in a) {for(l=1;l<=b[i];l++){print i,a[i]/b[i]}}}' inputfile

The awk script:{ l[NR] = $1; n[$1]++; s[$1] += $2; }
END {
for (i in n) { a[i] = s[i] / n[i]; }
for (i = 1; i <= NR; i++) { print l[i], a[l[i]]; }
}Results in:Test1 7.5
Test1 7.5
Test2...

If you have problem with the used memory you can try this:
awk '{
getline line < "file1"
gsub("[A-Za-z]","",line)
n=length(line)
$(n+1)="_"
sub(" _.*","")
}1' file2

awk 'NR==FNR{T[NR]=length($1);next}
{if (FNR%2) {print $0}
else {{for (i=1;i<T[FNR];i++) printf "%s ",$i}; printf "\n"}
}' file1 file2