What is Standard: Definition and 1000 Discussions

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. 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.
Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter sigma σ, 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. 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 unit as the data.
The standard deviation of a population or sample and the standard error of a statistic (e.g., of the sample mean) are quite different, but related. The sample mean's standard error is the standard deviation of the set of means that would be found by drawing an infinite number of repeated samples from the population and computing a mean for each sample. The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample size, and is estimated by using the sample standard deviation divided by the square root of the sample size. For example, a poll's standard error (what is reported as the margin of error of the poll), is the expected standard deviation of the estimated mean if the same poll were to be conducted multiple times. Thus, the standard error estimates the standard deviation of an estimate, which itself measures how much the estimate depends on the particular sample that was taken from the population.
In science, it is common to report both the standard deviation of the data (as a summary statistic) and the standard error of the estimate (as a measure of potential error in the findings). By convention, only effects more than two standard errors away from a null expectation are considered "statistically significant", a safeguard against spurious conclusion that are really due to random sampling error.
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).

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  1. A

    A Standard error of the coefficient of variation

    What is the standard error of the coefficient of variation in an exponential distribution?
  2. Dario56

    Standard Activity in Electrochemistry

    In the textbook Electrochemical Systems by Newman and Alyea, chapter 14: The definition of some thermodynamic functions, chemical potential of component (ionic or neutral) is written as a function of absolute activity: $$ \mu_i = RTln(\lambda_i) \tag {1} $$ where ##\lambda_i## is the absolute...
  3. DomDominate

    B What exactly is spin? Does the standard model work without spin?

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  4. O

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  5. chwala

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  6. Graham87

    I Basic standard deviation calculation

    I don’t get how they got the equation for the standard deviation. Why do they only square with the time in the denominator? Thanks!
  7. D

    Calculations using the Standard Solar Model & Solar Equations of State

    Assuming the Sun’s core has a mass of 0.35 Msolar_mass and taking values for other quantities from a internet background search or from the following figures (i.e.: Radius "solar core" = 0.25 Rsolar_radius ): ------------------------------------------------------------------------...
  8. A

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  9. danielcmk

    B Is the Standard Model overfitted?

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  10. patric44

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  11. S

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  12. shivajikobardan

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  13. alexandrinushka

    B Differences in Predictions between SR and LR?

    SR interpreted as having no absolute frame of reference and an absolute frame type version of SR, where the speed of light is isotropic only in one undetectable frame are considered equivalent, since they use the same math. But here is a scenario in which I don't see how the physical predictions...
  14. Sphere

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  15. Nikkie

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  16. J

    A The Generalized Capabilities of the Standard Model Lagrangian?

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  17. W

    B Why are SU(3), SU(2) and U(1) groups used in the Standard Model?

    hi, i have studied Standard Model for particle physics - at present it is described by three groups - i have studied - these groups but could not establish what particular feature suggest of these group to be used to describe SM. Thanks
  18. Zuzana

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  19. rstor

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  20. Jehannum

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  21. Buzz Bloom

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  22. P

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  23. Haorong Wu

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  24. J

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  25. chwala

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  26. nomadreid

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  27. L

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  28. resurgance2001

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  29. U

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  30. karush

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  32. M

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  33. C

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  34. N

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  35. N

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  36. I

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  37. M

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  38. Athenian

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  39. JD_PM

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  40. abnerko1973

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  41. A

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  42. lomidrevo

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  43. ChrisVer

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  44. Andrea Vironda

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  45. Addez123

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