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Discovered by Abraham de Moivre (1667-1754) when he noticed that many phenomena cluster around an average value and in so doing form a bell shaped curve. The heights of Canadians for examples cluster around the average height and if all heights were graphed a bell shaped curve would appear. The normal curve is a similar idea, and has a similar shape, but is a theoretical curve (or one derived from mathematical manipulation rather than observation) and was developed by Friedrich Gauss (1777-1855) to depict the effects of random variation. For example, if you collect 100 samples from a population in which you know the average value of a phenomenon (eg: support for a political party), the means of the 100 samples will cluster around the true mean (the population mean) according to the characteristics of the normal curve. The normal curve is symmetrical so that if we draw a line from the highest point of the curve to the base, half of the curve will lie on one side and half on the other. Further approximately 68% of the area of the entire curve is located between lines drawn at plus and minus one standard deviation (a standardized amount of deviation from the mean), and 95% of the area of the curve lies between lines drawn at plus and minus 2 standard deviations. In the example of drawing 100 samples from a population it can now be said that 95 of the means obtained from these samples will fall within plus or minus 2 standard deviations of the true mean. Once the calculation of standard deviation is learned one can then calculate the sampling error when doing sampling and estimate the value of a phenomenon in a population based on one sample. This is what is implied when an opinion poll in the newspaper reports that ‘a sample of this size is accurate to within plus or minus x%, 19 times out of 20’ (i.e., 95% of the time).

Last updated 2002--0-9-

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Athabaca University ICAAP

© Robert Drislane, Ph.D. and Gary Parkinson, Ph.D.
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