Gen weighted standard deviation4/1/2024 A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.įor example, the average height for adult men in the United States is about 70ins}}, with a standard deviation of around 3|ins. It shows how much variation there is from the "average" (mean). Standard deviation is a widely used measure of the variability or dispersion, being algebraically more tractable though practically less robust than the expected deviation or average absolute deviation. In probability theory and statistics, the standard deviation of a statistical population, a data set, or a probability distribution is the square root of its variance. File:Standard deviation illustration.gifĪ data set with a mean of 50 (shown in blue) and a standard deviation (σ) of 20. ![]() ![]() Each colored band has a width of one standard deviation. A plot of a normal distribution (or bell curve).
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