# The Guessing Game

## Physicists Recommend Ways to Make Better Educated Guesses: Look at the Overall Picture, Not Details

June 1, 2010

Physicists shared their tips for making a better educated guess when it comes to mathematical estimations. For example, the common contest of guessing the number of jelly beans in a jar is not best approached by attempting to count every visible jelly bean. Instead, experts suggest counting the number of beans in one row and then multiplying that by the number of layers in the jar. A broader approach is more effective than getting tied up in the smaller details.

## Science Insider

MATH IN EVERYDAY LIFE: People respond positively to very big numbers, so an internet provider might run a promotion offering 1025 hours of free Internet access. The small print reveals the offer is only good for 45 days. There are 1080 hours in 45 days, so customers would have to use their Internet access nearly 24/7 in order to take full advantage of the offer. Similarly, a food label that says a product is "90% fat free" will be more appealing than one that says it has "10% fat." People also lend more credence to exact numbers, preferring "50%" to the less specific "half." But it's easy to confuse precision with accuracy, such as with food packaging. Compare a soft drink that has 39 grams of sugar and 140 calories per serving to a fruit drink with 31 grams of sugar and 120 calories. But the serving size of the soft drink is 12 ounces, while the fruit drink is only 8 ounces. So ounce for ounce, the soft drink has fewer calories and less sugar than the fruit drink. A little math can help cut through the deception to obtain the information people want.

ESTIMATION: There are several tricks people can use to improve the accuracy of their estimations. Think about a way to count something that stands in for the whole, and how the volume of that piece relates to the larger volume. Want to know how many gallons of water are in a swimming pool? You need to assemble some information -- 500 gallons of water fills a volume of around 67 cubic feet. This is roughly a cube 4 feet on a side. If the pool is 20 feet by 60 feet and 4 feet deep throughout, that's 5 cubes by 15 cubes. You'd need to multiply 500 by 15 by 5 and find your estimate of 37,500 gallons of water. Quick, what's 18% of a \$33.42 restaurant bill? Move the decimal point one spot to the left and you'll get 10%, or \$3.34, and then half that figure again is \$1.67. Add them together. A 15% tip is about \$5, and a 20% tip is 2 times 10%, about \$6.60. In the middle, of course, lies 18%. The real answer is \$6.02, but you can get a decent estimate without using a calculator.

The American Mathematical Society, the Mathematical Association of America, and the American Physical Society contributed to the information contained in the TV portion of this report.

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Making a Guess

To Go Inside This Science:
Lawrence Weinstein
Old Dominion University
Norfolk, VA 23529
757 683 5803
weinstein@odu.edu

Mike Breen and Annette Emerson
American Mathematical Society
Providence, RI 02904-2294
paoffice@ams.org
1-800-321-4267

Ivars Peterson
Mathematical Association of America
Washington, DC 20036-1358
ipeterson@maa.org
1-800-741-9415

James Riordon, Media Relations
American Physical Society
College Park, MD
301-209-3238
Riordon@aps.org