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Sunday, April 05, 2009

The science of “guesstimation”

The latest National Geographic Science column on Mind Games shows a jar of jelly beans (presumably provided by the Easter bunny) and it offers a formula for estimating the number:

1. Count the jars radius (r) in beans. (This is hard to see due to the angle of the picture, but let’s say r equals 5.)
2. Estimate the height (h) in beans. (I can count this fairly easily from the photo – h equals 35.)
3. The volume (V) in beans is: V = 3 h r^2, where the constant 3 is a round-off on the circular constant pi. (So I estimate the beans in the National Geographic jar number 3x35x5^2, or 3x35x25 – the product of which is 2,625.)

The scientific, calculated estimate I made (2,625) for the count of jelly beans came a lot closer than my initial guess of ten thousand: The answer is 4,466. Going to all this effort might be worth it if you come across a bean-counting contest with a prize worth taxing your math skills.

Meanwhile, two professors at Old Dominion University in Virginia, one a mathematician (John Adam) and the other a physicist (Lawrence Weinstein), have teamed up to provide a primer on Guesstimation: Solving the World’s Problems on the Back of a Cocktail Napkin. As the publisher Princeton University Press says: “The ability to estimate is an important skill in daily life.”

As the father of five, I frequently was asked to help with math problems. First I’d ask that the student (my kid) work out a bottom-line number. Then I’d suggest they do a “reality check” by estimating the answer to at least the order of magnitude. That often sent them back to the beginning of the problem due to their first answer being so obviously wrong. The way facts and figures get thrown around the airwaves and internet nowadays it’s more important than ever to do reality checks.

I’ll bet this new book will be very helpful to equip reality checkers with the tools they need to achieve more accuracy. I learned about Guesstimation from its review in the March 31st New York Times. The Times article provides an interesting test of estimating ability: How many times does the American teenager say “like”? I heard this much more from my three daughters than my two sons, thus I hypothesize that there’s a gender bias. I’d hear this so word so over-used –- at least, like, once per sentence –- that I’d start counting them aloud, thus creating a great deal of aggravation for my teenager. I suppose the work “like” might come out ten times a minute and one hundred times per conversation. So I’m going to say a thousand “likes” per day could be in the realm of possibility. However, some teenagers are not afflicted by this word termite. My guess is ten thousand “likes” per year per teenager. To learn the answer, take this eight-question test of your estimation abilities.


  • At 12:47 PM, Anonymous Anonymous said…

    Clearly the radius is larger than 5 beans. Counting across the jar four times I got an average of 18.5 beans in a half circumference which divided by 3 (PI ish) is 6 and 1/6.

  • At 9:43 AM, Anonymous Anonymous said…

    I assume you are counting the radius in bean lengths and the height in bean diameters, but there is no accounting for the approximately hexagonal packing of the beans in 3-D space. I note that your estimate is shy of the answer by approximately the Golden Ratio of 1.618. Could this be due to the packing factor, or the ratio of the length to diameter of a jellybean, or just a coincidence?


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