Yesterday, after a long day, my wife and I settled in for some time to chill out, and turned on the TV. Although I’d never watch it on my own, I know my wife is a fan of watching The Biggest Loser, so I joined her for an episode last night. And to be completely fair, I think it’s a wonderful thing to help make people conscious about their bodies, their diet, their lifestyle, and how to have the life they want. The results of the people who succeed at this are truly spectacular.
They’re doing “couples” this season; there are mother-daughter teams, father-son, husband-wife, sisters, best friends, and cousins. Everyone started out — realistically — as morbidly obese, with no real direction as to how to improve themselves. But after 4 months or so of being at the compound (a.k.a. “We’re gonna train you to eat and exercise like a professional athlete”), people have lost anywhere from 95 to 145 pounds! Pretty impressive, no?
But they got towards the end of the episode, and my brain broke just a little bit. Here’s why: they have each person weigh-in, and they work the elimination criteria as follows:
- Everyone takes their weight from the previous week and weighs in, getting their weight for this week.
- They take the difference of those two numbers, and find the percentage of weight lost.
- They then rank everyone by percentage of weight lost, and the lowest two are eligible for elimination.
- The lowest two get voted on by the rest, and whomever is voted for by the majority goes home.
Pretty reasonable, except their method of measuring mass broke me, just a little. See if you can figure out why. The first four people weighed in, and here were their results (with weights in pounds):
|Name||Old Weight||New Weight||Weight Lost||% Lost|
Now, at this point, I’m jumping up and down and yelling at the television. “Doesn’t anybody understand significant figures?!” No, no they don’t, and here’s why. It looks like Tara lost the greatest percentage of weight; 2.15% is certainly more than 2.02%, 1.98%, and 1.95%, right? But none of these numbers mean anything; all we can say is that everyone lost 2% of their weight. Here’s why.
Let’s say Tara didn’t lose 4.00 pounds. Let’s say she lost 3.55 pounds instead. 3.55 rounds up to 4 pounds, but what if we calculated those numbers for 3.55 pounds lost? Well, that’s only 1.91% lost, which means she should be eligible for elimination. What if Ron, the lowest person here (percentagewise), actually lost 6.45 pounds? That would give him 2.09% lost, which would make him safe from elimination.
But the person who has it toughest is Filipe. Because Filipe weighs four more pounds than Mike, he has to lose an entire extra pound more than Mike to beat him under this system. If you’re going to eliminate people based on this insane “rounding off” formula, may I make a suggestion?
Oh my God, NBC! Get a scale that can measure to tenth-of-a-pound accuracies! Or hundredth of a pound, if that’s what you need. Here’s the math you need to know:
If you’re going to report a %-of-weight-lost to X significant digits, you need to measure the amount of weight lost to X significant digits.
So if you want to report 1.95% weight loss, you need your weights to be measured to the nearest hundredth of a pound. Otherwise, the game isn’t fair simply because of how you’re rounding off!