Standard deviation

MedPage Today  Sep 21  Comment 
(MedPage Today) -- It makes a difference -- sometimes a very big and important difference
Clusterstock  Dec 2  Comment 
Standard deviation is a concept that's thrown around frequently in finance. So what is it? When working with a quantitative data set, one of the first things we want to know is what the "typical" element of the set looks like, or where the...
EconMatters  Jun 29  Comment 
By  JW Jones I recently discussed the ability to use implied volatility to calculate the probability of a successful outcome for any given option trade. To review briefly, the essential concepts a trader must understand in order to make use of...
Clusterstock  Apr 21  Comment 
With the market totally shrugging off any of the recent ructions, David Rosenberg of Gluskin-Sheff turns his attention to the simple question of valuation. According to the Shiller P/E ratio, the S&P 500 is now 35% overvalued — a full one...
Index Universe  Nov 14  Comment 
The idea that standard deviation is an appropriate measure of risk for "real" investors is absurd. The problem (or rather, one of the problems) with standard deviation is that it largely ignores outliers, or minimizes their importance,...
Canadian Financial DIY  May 5  Comment 
Retired mathematician and investment aficionado Gummy (see link to his great website in my Resources sidebar on the right) wrote a provocative entry (see the lower part titled Correlation means ... what?) on his website in which he casts doubt on...


Standard deviation is a widely used measurement of variability or diversity used in statistics and probability theory. It shows how much variation or 'dispersion' there is from the 'average' (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large range of values.

Technically, the standard deviation of a statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler though practically less robust than the expected deviation or average absolute deviation. A useful property of standard deviation is that, unlike variance, it is expressed in the same units as the data. Note, however, that for measurements with percentage as unit, the standard deviation will have percentage points as unit.

In addition to expressing the variability of a population, 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. The reported margin of error is typically about twice the standard deviation–the radius of a 95% confidence interval. In science, researchers commonly report the standard deviation of experimental data, and only effects that fall far outside the range of standard deviation are considered statistically significant—normal random error or variation in the measurements is in this way distinguished from causal variation. Standard deviation is also important in finance, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.

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