In science, researchers commonly report the standard deviation of experimental data, and only effects that fall far outside the range of standard deviation are considered statistically significant – normal random error or variation in the measurements is in this way distinguished from causal variation. The reported margin of error is typically about twice the standard deviation – the radius of a 95 percent confidence interval. For example, the margin of error in polling data is determined by calculating the expected standard deviation in the results if the same poll were to be conducted multiple times. In addition to expressing the variability of a population, standard deviation is commonly used to measure confidence in statistical conclusions. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data. It is algebraically simpler though practically less robust than the average absolute deviation. The standard deviation of a statistical population, data set, or probability distribution is the square root of its variance. 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 points are spread out over a large range of values. It shows how much variation or “ dispersion” there is from the average ( mean, or expected value). Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. Red population has mean 100 and SD 10 blue population has mean 100 and SD 50. Example of two sample populations with the same mean and different standard deviations.
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