MythBusters Math Mix-up

My family members are huge fans of MythBusters. Like many viewers we sometimes question the finer points of their science and their tests, but that leads to healthy discussions so it all works out quite nicely. However in a recent episode (originally aired May 19, 2010) they made a math mistake that left us scratching our heads.

In this episode they investigate the Left Hand Turn myth to see whether delivery trucks can save fuel by avoiding left turns and the wasteful idling while waiting to turn – see http://en.wikipedia.org/w/index.php?title=MythBusters_(2010_season)#Left_Hand_Turn

However after a couple of days of carefully measuring fuel consumption on two different routes they made an odd math error. On both routes the percentage difference that they listed were too small – by about a factor of ten!

The results for the first test are shown at the 5:05 mark of www.youtube.com/watch?v=G9F0YUqsihA and are screen grabbed here:

They verbally describe the percentage as being about 0.4%, and you can see above that they summarize that as being less than 1%. But that doesn’t even pass the smell test. 1% means one per hundred. One percent of 226 is 2.26, one percent of 22.6 is 0.226, and one percent of 2.26 is 0.0226. But the difference in fuel consumption that they measured is 0.08 lbs. Last I checked 0.08 is bigger than 0.0236 – more than three times bigger.

The math for calculating the percentage difference between two numbers is pretty simple: take the difference between them, divide it by one of the numbers, and multiply by one hundred to convert to percentage. In other words x = ((n2 – n1) / n1) * 100. You can then say that n2 is x% greater or smaller than n1. So we have:

((2.26 – 2.34) / 2.34) * 100 = -3.39, so 2.26 is 3.39% smaller than 2.34.

3.39% is more than a 1% difference. Alternately we can reverse the numbers and go:

((2.34 – 2.26) / 2.26) * 100 = 3.54, so 2.34 is 3.54% greater than 2.26.

3.54% is also more than a 1% difference.

The results for their second test can be seen at the 6:57 mark of www.youtube.com/watch?v=RMpUzU0esPs and are screen grabbed here:

Again, their percentage calculation doesn’t pass the 6th grade sanity check. It’s obvious if you think about it that 4.0 lbs is at least one third less than 6.8 lbs, and one third is about 33%, so 3% makes no sense. Doing the math we can see:

((4.0 – 6.8) / 6.8) * 100 = -41.2, so 4.0 is 41.2% less than 6.8.

Their percentage difference is more than thirteen times too small!!! Again we can try the reverse calculation and go:

((4.0 – 6.8) / 6.8) * 100 = 70, so 6.8 is 70% more than 4.0.

Since they were talking about how much smaller 4.0 is than 6.8 the first calculation is the correct one and the results can be summarized as “4.0 is 41.2% less than 6.8.”

I’m not sure how they managed to make this mistake. Maybe they multiplied by ten instead of by one hundred? If so they need to go back to both math class and French class (cent is French for one hundred).

Myth: The Mythbusters think that “percentage” means “per ten”.

Confirmed!

I’m surprised that they made this mistake and I’m surprised that nobody noticed it during editing. I’m also surprised that I can’t find any evidence that anybody else has called them on this.

The two videos (part 1 and part 2 of this myth) can be seen here, so that you can check for yourself:

MythBusters–Left Hand Turn part 1 of 2

MythBusters–Left Hand Turn part 2 of 2