Need some help with math...

I was at a training meeting today, and was really grilled by another consultant.  I'm very interested in understanding my "flawed thinking."  It was an elementary grade level problem/task. 

Here's the situation.  There are 6 brown paper sacks with colored squares inside (the number wasn't given).  One was labeled "Hector" and the other 5 were labled A-E.  The goal was to find Hector's mother by comparing experimental data (drawing squares one at a time with replacement) for the 6 sacks.

I ruled out two "mothers" right away based on an initial trial of drawing and replacing tiles 40 times from each sack.  The other three were close to Hector, so I drew 20 more times and eliminated one more "mother."  So, here's the my experimental data...

Hector was (on average) 50% red tiles drawn, 25% blue, and 25% green.

Maria was 67% red, 18% blue, 15% green

Grace was 34% red, 33% blue and 33% green

Which is closest?  In my thinking, I needed to find a way to decide who was closest to Hector.  If Hector were 60, 20, 20, Maria 80, 10, 10, and Grace 40, 30, 30, who is closest?  That was my struggle.  I was pressured to make a decision based on time.  To make a choice, I subtracted the difference of each percent.

Comparing Hector and Maria, difference red 17, blue 7, green 10 for a total of 34.

Comparing Hector to Grace, difference red 16, blue 8, green 8 for a total of 32.  I decided Grace was more likely to be the mother. 

I was grilled in front of 30 other people about why I chose to look at differences, as that is not a good comparison when considering proportionality.  I chose Grace, but others said it should be Maria because the shape of their graphed results (bar graphs) looked more similar (tall, short, short).  Can anyone explain this to me?

Thanks, Kelly

PS, I'm willing to answer any questions you may have to help clarify the problem.

I need some more info about the situation. I'm not understanding the "mothers" thing. Is Hector's mom one of the 5 labeled A through E?
When I reread it, it seems that Maria would have been closer. I think your estimation of Maria being 80-10-10 was a little high. With Grace, it seemed that with your %, red, blue and green were equally likely to have occured. Hector was predominantly red, with blue and green being equally likely. Maria follows that same pattern closer than Grace.

Again, I'm not exactly sure of the situation and if I'm thinking of it correctly.

Hope this helps. :)

Yep, one of the 5 is the mom.  It also makes sense to me that Grace's colors seem equally likely, where Hector's weren't.  But, then I think, that his proportions didn't really match Maria that well either.  I wasn't really saying Maria was 80-10-10, but was posing a "what if" situation.  If we were comparing 60-20-20 as what we wanted, and drew 80-10-10, and 40-30-30, which would be the most likely match?  How do we decide?  Thanks for the reply.  I wasn't sure anyone was going to.  I'm not out to prove I'm right, just need to clarify it in my mind.