Interesting I wonder how far this extends? Could make an interesting paper in Ed Psych or something. e.g I think most adults could find the exact average of 2 numbers where the differnce is 2. How many could do it if the difference were 4? 3? 6? 10? My bet would be that a diff. of 10 would be easier for many than a diff. of 4, and that 3 would be much harder.
Also, finding a center when the numbers are about equal seems easy; what if they are a little spread out? Or a lot spread out? What if you asked a bunch of people to average 10 11 12 13 14 100,000 ? Peter Peter L. Flom, PhD Assistant Director, Statistics and Data Analysis Core Center for Drug Use and HIV Research National Development and Research Institutes 71 W. 23rd St www.peterflom.com New York, NY 10010 (212) 845-4485 (voice) (917) 438-0894 (fax) >>> [EMAIL PROTECTED] 2/20/2004 8:44:27 PM >>> Which reminds me of a story. I gave a student two numbers (say, 376 and 378) and asked him the average. He answered 377, quick as a flash. Then I asked him how he calculated the average, and he said, quick as a flash, add the numbers and divide by two. Then I asked him what was 376 + 378. He couldn't do that without pencil and paper. So he wasn't adding the numbers. I thought for a while how he actually did figure out the average. I thought about the possibility that he stripped off the front numbers, added 6 + 8, divided by two, and then restored the front numbers. I don't think he knew math well enough to do that, or that he could do those calculations as quickly as he could know the average. Also, I don't think he would have had trouble with the average of 999 and 1001 (assuming he knew they were two apart). My memory is that this worked with several students, and anyway it works on me -- I can tell you the average of 376 and 378 without doing any addition, and the answer comes so fast it is not easy for me to know what I am doing. I think this generalizes to more numbers. If I give you a set like <62, 69, 72, 58, 64, 69, 61, 57> you can give me a rough estimate of the average without doing any addition. You have a lot of statistical expertise, but I think anyone could do it. Or at least anyone could do it if I asked about the center. If I graphed the numbers out, it would probably be even easier. So I guess I am talking about some very primitive ability to find the center, somehow without adding. We call it average, fine, but that might disconnect average from the student's idea of center, and then when average is defined by a formula and the formula involves adding the numbers, they might think that the more numbers there are, the higher the average. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
