awk if with variables doesn't work properly sometimes

In a text, I want to classify my data according to it range.

For example, 8.1,9.1,9.9 are all in [8,10). I used variables called left and right to replace 8 and 10 respectively in awk-if. But it doesn't work properly.

My data like this:

9.1 aa
9.2 bb
10.1 cc
11.9 dd

Then my scripts like this:

left=8;right=10                    #left=10;right=12
echo "["$left","$right"]:"
cat data | awk '{if(($1>="'$left'")&&($1<"'$right'")) print $2}' | xargs

The result is empty.

[8,10]:

But if I use 8 and 10 directly (without variables), it's OK. And when I use left=10, right=12, it works also properly.

I also found when left=98, right=100, it also didn't work. So why sometimes it doesn't work? Thanks a lot!