(en.wikipedia.org) Standard deviation - Wikipedia

ROAM_REFS: https://en.wikipedia.org/wiki/Standard_deviation

In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an outlier and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.) A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. Standard deviation can also be used to calculate standard error for a finite sample, and to determine statistical significance.

When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).

Confidence Proportion within Proportion without Proportion without
interval Percentage Percentage Fraction
0.318639σ 25% 75% 3/4
0.674490σ 50% 50% 1/2
0.977925σ 66.6667% 33.3333% 1/3
0.994458σ 68% 32% 1/3.125
68.2689492% 31.7310508% 1/3.1514872
1.281552σ 80% 20% 1/5
1.644854σ 90% 10% 1/10
1.959964σ 95% 5% 1/20
95.4499736% 4.5500264% 1/21.977895
2.575829σ 99% 1% 1/100
99.7300204% 0.2699796% 1/370.398
3.290527σ 99.9% 0.1% 1/1000
3.890592σ 99.99% 0.01% 1/10000
99.993666% 0.006334% 1/15787
4.417173σ 99.999% 0.001% 1/100000
4.5σ 99.9993204653751% 0.0006795346249% 1/147159.5358\\ 6.8/1000000
4.891638σ 99.9999% 0.0001% 1/1000000
99.9999426697% 0.0000573303% 1/1744278
5.326724σ 99.99999% 0.00001% 1/10000000
5.730729σ 99.999999% 0.000001% 1/100000000
99.9999998027% 0.0000001973% 1/506797346
6.109410σ 99.9999999% 0.0000001% 1/1000000000
6.466951σ 99.99999999% 0.00000001% 1/10000000000
6.806502σ 99.999999999% 0.000000001% 1/100000000000
99.9999999997440% 0.000000000256% 1/390682215445

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