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.