
related topics 
{rate, high, increase} 
{math, number, function} 
{game, team, player} 
{car, race, vehicle} 
{city, population, household} 
{company, market, business} 
{island, water, area} 
{math, energy, light} 

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 average absolute deviation.^{[1]}^{[2]} 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 deviationâ€“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 significantâ€”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.
When only a sample of data from a population is available, the population standard deviation can be estimated by a modified quantity called the sample standard deviation, explained below.
Contents
Full article ▸


related documents 
Minimum wage 
Labour economics 
Flat tax 
Poker probability 
Variance 
Purchasing power parity 
Poverty 
Pension 
Land value tax 
General equilibrium 
401(k) 
Full employment 
Student's tdistribution 
Maximum likelihood 
Indifference curve 
Utility 
Intelligence quotient 
Medicare (United States) 
Sixteenth Amendment to the United States Constitution 
Interest 
SAT 
Statistical hypothesis testing 
Stagflation 
Likelihood function 
New Keynesian economics 
IS/LM model 
Externality 
Carbon tax 
Economic growth 
Tax Reform Act of 1986 
