Standard deviation | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-07

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Standard_deviation


00:02:48 1 Basic examples
00:02:58 1.1 Sample standard deviation of metabolic rate of northern fulmars
00:05:16 1.2 Population standard deviation of grades of eight students
00:07:24 1.3 Standard deviation of average height for adult men
00:11:50 2 Definition of population values
00:12:39 2.1 Discrete random variable
00:14:27 2.2 Continuous random variable
00:17:41 3 Estimation
00:21:25 3.1 Uncorrected sample standard deviation
00:23:19 3.2 Corrected sample standard deviation
00:24:47 3.3 Unbiased sample standard deviation
00:27:19 3.4 Confidence interval of a sampled standard deviation
00:31:13 3.5 Bounds on standard deviation
00:33:21 4 Identities and mathematical properties
00:35:13 5 Interpretation and application
00:37:50 5.1 Application examples
00:38:50 5.1.1 Experiment, industrial and hypothesis testing
00:44:14 5.1.2 Weather
00:46:24 5.1.3 Finance
00:46:42 5.2 Geometric interpretation
00:48:16 5.3 Chebyshev's inequality
00:48:57 5.4 Rules for normally distributed data
00:52:36 6 Relationship between standard deviation and mean
00:52:55 6.1 Standard deviation of the mean
00:54:23 7 Rapid calculation methods
00:54:50 7.1 Weighted calculation
00:58:17 8 History
00:58:22 9 See also
01:00:00 10 References
01:03:16 11 External links
01:07:57 Weighted calculation
01:11:58 History



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SUMMARY
=======
In statistics, the standard deviation (SD, also represented by the lower case Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.
The standard deviation of a random variable, statistical population, data set, or probability distribution is the square root of its variance.  It is algebraically simpler, though in practice less robust, than the average absolute deviation.
A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. 
In addition to expressing the variability of a population, the standard deviation is commonly used to measure confidence in statistical conclusions.  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.  This derivation of a standard deviation is often called the "standard error" of the estimate or "standard error of the mean" when referring to a mean.  It is computed as the standard deviation of all the means that would be computed from that population if an infinite number of samples were drawn and a mean for each sample were computed.
It is very important to note that the standard deviation of a population and the standard error of a statistic derived from that population (such as the mean) are quite different but related (related by the inverse of the square root of the number of observations). The reported margin of error of a poll is computed from the standard error of the mean (or alternatively from the product of the standard deviation of the population and the inverse of the square root of the sample size, which is the same thing) and is typically about twice the standard deviation—the half-width of a 95 percent confidence interval.  
In science, many researchers report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant—normal random error or variation in the measurements is in this way distinguished fro ...