quartz/content/Obsidian Vault/remnote backup/why square and then square root when getting standard deviation??.md

• the alternative is called mean absolute deviation - \frac {\sum (x- \bar x)}{n}
• instead of standard deviation - \sqrt \frac{\sum (x- \bar x)^2}{n-1}
• reasons:
  • In an earlier era of computation it seemed easier to find the square root of one figure rather than take the absolute values for a series of figures. This is no longer so, because the calculations are done by computer.
  • In those rare situations in which we obtain full response from a random sample with no measurement error and wish to estimate, using the dispersion in our sample, the dispersion in a perfect Gaussian population, then the standard deviation has been shown to be a more stable indicator of its equivalent in the population than the mean deviation has. Note that we can only calculate this via simulation, since in real-life research we would not know the actual population figure
  • modern statistics is largely built on top of the standard deviation.
  • http://www.leeds.ac.uk/educol/documents/00003759.htm