Q: Standard deviation formula

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Standard deviation is a way to describe how the data is distributed around the Arithmatic Mean. It is not a simple formula to calculate, as shown in the links.

Standard deviation is a way to describe how the data is distributed around the Arithmatic Mean. It is not a simple formula to calculate, as shown in the links.

100 x (standard deviation/mean)

Usually, industrial use of standard deviation is involved in quality control and testing. A product such as cement, is produced in batches, and I assume, requires periodic testing to ensure consistent properties. The sample test variations can be evaluated using standard deviation. If the standard deviation is high, it is likely that inferior product could be shipped. Probability analysis can determine the chance that product below certain standards would be shipped.

If a variable X, is distributed Normally with mean m and standard deviation s thenZ = (X - m)/s has a standard normal distribution.

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Standard deviation is a way to describe how the data is distributed around the Arithmatic Mean. It is not a simple formula to calculate, as shown in the links.

Arithmatic Mean

b-a/6

The formula for standard deviation has both a square (which is a power of 2) and a square-root (a power of 1/2). Both must be there to balance each other, to keep the standard deviation value's magnitude similar to (having the same units as) the sample numbers from which it's calculated. If either is removed from the formula, the resulting standard deviation value will have different units, reducing its usefulness as a meaningful statistic.

Standard deviation (SD) is neither biased nor unbiased. Estimates for SD can be biased but that depends on the formula used to calculate the estimate.

100 x (standard deviation/mean)

Coefficient of deviation (CV) is a term used in statistics. It is defined as the ratio of the standard deviation (sigma) to the mean (mu). The formula for CV is CV=sigma/mu.

Formula for standard error (SEM) is standard deviation divided by the square root of the sample size, or s/sqrt(n). SEM = 100/sqrt25 = 100/5 = 20.

It is a bit complicated; you can find the details here: http://en.wikipedia.org/wiki/Standard_deviation

No, a standard deviation or variance does not have a negative sign. The reason for this is that the deviations from the mean are squared in the formula. Deviations are squared to get rid of signs. In Absolute mean deviation, sum of the deviations is taken ignoring the signs, but there is no justification for doing so. (deviations are not squared here)

Usually, industrial use of standard deviation is involved in quality control and testing. A product such as cement, is produced in batches, and I assume, requires periodic testing to ensure consistent properties. The sample test variations can be evaluated using standard deviation. If the standard deviation is high, it is likely that inferior product could be shipped. Probability analysis can determine the chance that product below certain standards would be shipped.