I guess the thing about numbers is that people assume they understand them... they are condensed versions of images, explanations, captions and all the rest.
I don't think you can accuse me of trying to trick people. I put the key information in the question itself, it's not buried or weak.
The reason people get this wrong (and in fact get really angry at me when they do) is because they think they are manipulating the truth when they're messing with the numbers, but they're not. They're averaging averages.
A car drives from NY to Buffalo at 60 miles an hour. It drives back at 40 miles an hour.
What's the average speed?
Hint: it's not 50, and my wording isn't weak. We're just not that good at turning numbers into truth.
Zack Grossbart
· 4 months ago
@Seth This is a really good example of how emotional people can get about numbers. As an engineer I would like to believe that numbers are emotionless, but that just isn't the case. The way data is presented has an enormous impact on the way that data is perceived.
That said, I didn't mean to imply that you were trying to trick anyone or had any malicious intent. Your example showed very well how easily you can change impressions by changing the way something is presented. I wanted to show an example that reversed the effect you were creating.
One of the problems with telecommuting is that people often misrepresent data accidentally and create unnecessary communication problems. This happens everywhere, but being far away from your team means you need to put extra effort into resolving these issues.
...and thank you for being the first commenter on this new blog.
P.S. Let's start by assuming we are talking about New York city instead of New York state. You don't say how long the journey took, but we'll say it took one hour to get there and therefore 1.5 hours to get back since the time doesn't change the average. That means you traveled for 2.5 hours and went 120 miles. 120 / 2.5 = an average speed of 48 miles per hour.
Teri Abel
· 4 months ago
Your explanation is great and the little cars/SUVs rock. Seth got a back rub compared to the irate reactions Marilyn Vos Savant got upon similarly offending peoples' mathematical intuition in the famous "Two boys" problem (got statistics?) I entertained on my blog.
Zack Grossbart
· 4 months ago
Thanks for the comment Teri. Statistics problems offer many chances for seemingly obvious wrong answers. The two boys problem makes me think of the birthday problem.
Mike
· 3 months ago
If you want people to get REALLY mad at numbers, introduce them to the Monty Hall Problem.
Helen
· 2 months ago
I thought your explication of this problem was excellent. Your description made it clear what exactly it was that needed to be compared (gallons used rather than mpg), but it also highlighted the point you are making, that clarity of expression greatly enhances ease of communication. I deal remotely with an intern from another country whose English is not really bad, but whose constant use of long and involved sentences makes deciphering his meaning a lengthy ordeal .
All Comments
I don't think you can accuse me of trying to trick people. I put the key information in the question itself, it's not buried or weak.
The reason people get this wrong (and in fact get really angry at me when they do) is because they think they are manipulating the truth when they're messing with the numbers, but they're not. They're averaging averages.
A car drives from NY to Buffalo at 60 miles an hour.
It drives back at 40 miles an hour.
What's the average speed?
Hint: it's not 50, and my wording isn't weak. We're just not that good at turning numbers into truth.
That said, I didn't mean to imply that you were trying to trick anyone or had any malicious intent. Your example showed very well how easily you can change impressions by changing the way something is presented. I wanted to show an example that reversed the effect you were creating.
One of the problems with telecommuting is that people often misrepresent data accidentally and create unnecessary communication problems. This happens everywhere, but being far away from your team means you need to put extra effort into resolving these issues.
...and thank you for being the first commenter on this new blog.
P.S. Let's start by assuming we are talking about New York city instead of New York state. You don't say how long the journey took, but we'll say it took one hour to get there and therefore 1.5 hours to get back since the time doesn't change the average. That means you traveled for 2.5 hours and went 120 miles. 120 / 2.5 = an average speed of 48 miles per hour.