Unix bash scripting sort

I see that you ask for a Bash solution but since you tagged it also Unix I suggest a pure awk solution (awk is just ideal for such problems):

awk '
  {
    if(length($1) <= 3 && $1 ~ /^[0-9]+$/) {
      if($1 > MAX) {MAX = $1}
      SUM+=$1
      N++
      print $1, N, SUM
    } else {
      print "Illegal Input " $1
    }
  }
  END {
    print "Average: " SUM / N
    print "Max: " MAX
  }
' < <(echo -e "246\n321\n16\n10\n12345\n4\n274\n0")

prints

246 1 246
321 2 567
16 3 583
10 4 593
Illegal Input 12345
4 5 597
274 6 871
0 7 871
Average: 124.429
Max: 321

However, I cannot comprehend why the above input yields 145 as average?

tmpfile=`mktemp`
while read line ; do
  if [[ $line =~ ^[0-9]{1,3}$ ]] ; then 
    # valid input
    if [ $line == "0" ] ; then
      break
    fi  
    echo $line >> $tmpfile
  else 
    echo "ERROR: invalid input '$line'"
  fi  
done
awk ' { tot += $1; if (max < $1) max = $1; } \
  END { print tot / NR; print max; } ' $tmpfile
rm $tmpfile 

A piped coreutils option with bc:

echo 246 321 16 10 12345 4 274 0           \
| grep -o '\b[0-9]{1,3}\b'                 \
| tee >(sort -n | tail -n1 > /tmp/max)     \
| tr '\n' ' '                              \
| tee >(sed 's/ $//; s/ \+/+/g' > /tmp/add) \
      >(wc -w > /tmp/len) > /dev/null

printf "Max: %d, Min: %.2f\n" \
  $(< /tmp/max)               \
  $((echo -n '('; cat /tmp/add; echo -n ')/'; cat /tmp/len) | bc -l)

Output:

Max: 321, Min: 124.43

• grep ensures that the number format constraint.
• sort finds max, as suggested by chepner
• sed and wc generate the sum and divisor.

Note that this generates 3 temporary files: /tmp/{max,add,len}, so you might want to use mktemp and/or deletion:

rm /tmp/{max,add,len}

Edit

Stick this into the front of the pipe if you want to know about invalid input:

tee >(tr ' ' '\n'            \
      | grep -v '\b.{1,3}\b' \
      | sed 's/^/Invalid input: /' > /tmp/err)

And do cat /tmp/err after the printf.