What Field Studies Small Groups with a Characteristic?Date: 6/10/96 at 17:29:34 From: Anonymous Subject: What field studies small groups with a characteristic? I'm interested in knowing whether there is a field that studies the following or if there is a solution to this question. I have not been able to find any useful information in a textbook. 1. Take for example that person A has blonde hair. 2. You know that this person is not famous. 3. You also know that (10) people know person A. 4. You would like to know that if (10) people know person A, how many people in a given population also know someone like person A, someone with blonde hair. 5. You really want to know how many people with blonde hair there are in a given population given the answer to #4. Thank you. Date: 7/1/96 at 8:41:28 From: Doctor Moskowitz Subject: Re: What field studies small groups with a characteristic? Yes, there is certainly a branch of math that deals with these types of questions - it's Probability. Any question of determining information about a large number of objects (in this case people) from information about a smaller sample is the province of probability and statistics. In the case of your problem, you need to be a little more specific about some things. It makes a difference whether you ask if a person in the population "knows a person with blond hair" or ask if they know _exactly_one_ person with blond hair. In the latter case, if everyone knows ten people, and exactly one has blond hair, then 10% of the population are blondes. If the former is true, you'd need to find out exactly how many blondes each person knew to get a definite answer to your question. However, this is a more special case than you'd usually expect, since we somehow knew what every single person knew, and further knew that every single person knew exactly ten people. In the real world that's ridiculous, different people know different numbers of folks; even if nobody's "famous" there are still people who are known by more than others; you usually only have access to a certain small portion of the population. And that's where a huge amount of mathematics comes in -- the fields of probability and stat. The answers given to problems with uncertainties in them are themselves uncertain -- that is, there's a "most likely" answer, along with another number indicating how much that number might be off from reality. To get further info about statistics, you might want to check out http://olam.ed.asu.edu/~glass/502/home.html - it's an entire statistics course on the Web! -Doctor Moskowitz, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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