Tuesday, December 11, 2012

Recreational Statistics

At our Ward's Christmas party this year, they had a large jar of Hersey's candy kisses and we were asked to guess the total number. The closest guess to the actual number got to take them home. I remember reading a story about how in such situations, that the average of all the guesses would be closer to actual than the winning guess, a sort of accuracy through consensus thing. Here was my chance to test that out, so I volunteered to check the answers.

We had 72 guesses cast, and as we went through them, I could see the average would be low because some of the smaller kids had unrealistic guesses like 8 or 20. One kid wrote "there are 0 kisses in the jar, but some candy kisses". Funny, and true, but no chocolate for him. The winning guess was 454, which was about 8% higher than the 417 actual pieces. Robin had the next closest guess and was quite disappointed.

Days later, I plugged all the guesses into my magic bit box to see what the statistics said. The average, or mean, as I predicted was very low at 208. That indicated an abnormal distribution, which a histogram quickly confirmed. Somewhere in my reading, I came across a tidbit that said the median would be a better statistic to use for a skewed distribution. Sure enough, the median is 407, or about 3% off actual, and much closer than the winning guess. So I guess with a little quibbling about the use of mean or median, the story was right.

I tracked down the story, and it is from a book called "The Wisdom of Crowds", and involves guessing the weight of an ox at the county fair. I'd rather have chocolate.

Fun Facts: Hershey's Kisses were introduced in 1907, but the term "KISSES" wasn't trademarked until 2001. Hershey makes more than 60 million kisses a day. Candy kisses that is.


Eldon and Janeil Olsen said...

Ken, what a cool histogram. But, isn't the median the number with half of the guesses higher and half lower. It looks to me like that number is even lower than the mean. In any case it sounds like Robin has a bright future in weather forecasting. Dad/

PS Did you know that one of my minors in my Phd was statistics.

Ken said...

That is what I get for publishing without peer review. That changes the outcome of the narrative. Retraction!