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Bell Curve

Alex Bierman

Subject Sociology » Methods in Sociology

Key-Topics quantitative methods

DOI: 10.1111/b.9781405124331.2007.x


Extract

The bell curve, also known as the normal distribution, provides a foundation for the majority of statistical procedures currently used in sociology. It can be thought of as a histogram of a continuous variable, but with such fine distinctions between outcomes that it is not possible to differentiate individual bars, so that the histogram appears to be a smooth line in the shape of a bell. Beneath this line is 100 percent of the possible outcomes, with the x -axis describing the range of possible outcomes and the y -axis describing the proportion or probability for each outcome. The shape of the distribution is symmetrical, so that if it is divided in two, one half is the mirror image of the other. It is also unimodal, meaning that there is only one mode (most frequent value in the distribution). Because the bell curve is unimodal and symmetrical, the distribution's mean, median, and mode are identical and in the exact center of the distribution. Additionally, the “tails” of the curve extend indefinitely, without ever actually reaching the x -axis. The bell curve has a specific distribution of scores. One standard deviation from the mean will always take up 34.13 percent of the area under the curve, or 34.13 percent of scores for the variable. Two standard deviations from the mean will always take up 47.72 percent of the area under the curve. Three standard deviations will always ... log in or subscribe to read full text

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