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- Standard_deviation abstract "In statistics, the standard deviation (SD, also represented by the Greek letter sigma, σ for the population standard deviation or s for the sample standard deviation) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard deviation close to 0 indicates that the data points tend to be very close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.The standard deviation of a random variable, 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 units as the data. There are also other measures of deviation from the norm, including mean absolute deviation, which provide different mathematical properties from standard deviation.In addition to expressing the variability of a population, the 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 half-width of a 95 percent confidence interval. In science, researchers commonly report the standard deviation of experimental data, and only effects that fall much farther than two standard deviations away from what would have been expected are considered statistically significant—normal random error or variation in the measurements is in this way distinguished from causal variation. The 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 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 a better estimate of the population standard deviation (the standard deviation of the entire population).".
- Standard_deviation thumbnail Standard_deviation_diagram.svg?width=300.
- Standard_deviation wikiPageExternalLink standard-deviation.appspot.com.
- Standard_deviation wikiPageExternalLink www.ifa.com.
- Standard_deviation wikiPageExternalLink stddev-30-secs.html.
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- Standard_deviation wikiPageRevisionID "683749841".
- Standard_deviation wikiPageWikiLink 68-95-99.7_rule.
- Standard_deviation wikiPageWikiLink 68–95–99.7_rule.
- Standard_deviation wikiPageWikiLink Accuracy_and_precision.
- Standard_deviation wikiPageWikiLink Algebra.
- Standard_deviation wikiPageWikiLink Algebraic_formula_for_the_variance.
- Standard_deviation wikiPageWikiLink Arithmetic_average.
- Standard_deviation wikiPageWikiLink Arithmetic_overflow.
- Standard_deviation wikiPageWikiLink Arithmetic_underflow.
- Standard_deviation wikiPageWikiLink Average.
- Standard_deviation wikiPageWikiLink Average_absolute_deviation.
- Standard_deviation wikiPageWikiLink Average_human_height.
- Standard_deviation wikiPageWikiLink Bessels_correction.
- Standard_deviation wikiPageWikiLink Bias_of_an_estimator.
- Standard_deviation wikiPageWikiLink Biased_estimator.
- Standard_deviation wikiPageWikiLink Bollinger_Bands.
- Standard_deviation wikiPageWikiLink CERN.
- Standard_deviation wikiPageWikiLink Calculus.
- Standard_deviation wikiPageWikiLink Carl_Friedrich_Gauss.
- Standard_deviation wikiPageWikiLink Category:Data_analysis.
- Standard_deviation wikiPageWikiLink Category:Statistical_deviation_and_dispersion.
- Standard_deviation wikiPageWikiLink Category:Statistical_terminology.
- Standard_deviation wikiPageWikiLink Category:Summary_statistics.
- Standard_deviation wikiPageWikiLink Cauchy_distribution.
- Standard_deviation wikiPageWikiLink Central_limit_theorem.
- Standard_deviation wikiPageWikiLink Central_moment.
- Standard_deviation wikiPageWikiLink Chebyshevs_inequality.
- Standard_deviation wikiPageWikiLink Chi_distribution.
- Standard_deviation wikiPageWikiLink Coefficient_of_variation.
- Standard_deviation wikiPageWikiLink Commutative_property.
- Standard_deviation wikiPageWikiLink Completing_the_square.
- Standard_deviation wikiPageWikiLink Computational_formula_for_the_variance.
- Standard_deviation wikiPageWikiLink Concave_function.
- Standard_deviation wikiPageWikiLink Confidence_interval.
- Standard_deviation wikiPageWikiLink Consistent_estimator.
- Standard_deviation wikiPageWikiLink Continuous_distribution.
- Standard_deviation wikiPageWikiLink Covariance.
- Standard_deviation wikiPageWikiLink Cumulant.
- Standard_deviation wikiPageWikiLink Cumulative_distribution_function.
- Standard_deviation wikiPageWikiLink Definite_integral.
- Standard_deviation wikiPageWikiLink Degrees_of_freedom_(statistics).
- Standard_deviation wikiPageWikiLink Descriptive_statistics.
- Standard_deviation wikiPageWikiLink Deviation_(statistics).
- Standard_deviation wikiPageWikiLink Dimensionless_number.
- Standard_deviation wikiPageWikiLink Dimensionless_quantity.
- Standard_deviation wikiPageWikiLink Distance_correlation.
- Standard_deviation wikiPageWikiLink Efficient_estimator.
- Standard_deviation wikiPageWikiLink Error_bar.
- Standard_deviation wikiPageWikiLink Error_function.
- Standard_deviation wikiPageWikiLink Estimator.
- Standard_deviation wikiPageWikiLink Excess_kurtosis.
- Standard_deviation wikiPageWikiLink Expected_value.
- Standard_deviation wikiPageWikiLink Gamma_function.
- Standard_deviation wikiPageWikiLink Geometric_standard_deviation.
- Standard_deviation wikiPageWikiLink Higgs_boson.
- Standard_deviation wikiPageWikiLink Human_height.
- Standard_deviation wikiPageWikiLink Integral.
- Standard_deviation wikiPageWikiLink Jensens_inequality.
- Standard_deviation wikiPageWikiLink Karl_Pearson.
- Standard_deviation wikiPageWikiLink Kurtosis.
- Standard_deviation wikiPageWikiLink Location_parameter.
- Standard_deviation wikiPageWikiLink Log-normal_distribution.
- Standard_deviation wikiPageWikiLink Mahalanobis_distance.
- Standard_deviation wikiPageWikiLink Margin_of_error.
- Standard_deviation wikiPageWikiLink Maximum_likelihood.
- Standard_deviation wikiPageWikiLink Mean.
- Standard_deviation wikiPageWikiLink Mean_absolute_deviation.
- Standard_deviation wikiPageWikiLink Mean_absolute_error.
- Standard_deviation wikiPageWikiLink Mean_squared_error.
- Standard_deviation wikiPageWikiLink Measurement.
- Standard_deviation wikiPageWikiLink Modern_portfolio_theory.
- Standard_deviation wikiPageWikiLink Moment_(mathematics).
- Standard_deviation wikiPageWikiLink Normal_distribution.
- Standard_deviation wikiPageWikiLink Normalizing_constant.
- Standard_deviation wikiPageWikiLink Opinion_poll.
- Standard_deviation wikiPageWikiLink Parametric_model.
- Standard_deviation wikiPageWikiLink Particle_physics.
- Standard_deviation wikiPageWikiLink Percentage_point.
- Standard_deviation wikiPageWikiLink Percentile.
- Standard_deviation wikiPageWikiLink Pooled_variance.
- Standard_deviation wikiPageWikiLink Prediction_interval.
- Standard_deviation wikiPageWikiLink Probability_density_function.
- Standard_deviation wikiPageWikiLink Probability_distribution.
- Standard_deviation wikiPageWikiLink Random_variable.
- Standard_deviation wikiPageWikiLink Rate_of_return.
- Standard_deviation wikiPageWikiLink Raw_score.
- Standard_deviation wikiPageWikiLink Relative_standard_deviation.
- Standard_deviation wikiPageWikiLink Risk.
- Standard_deviation wikiPageWikiLink Robust_measures_of_scale.
- Standard_deviation wikiPageWikiLink Robust_standard_deviation.
- Standard_deviation wikiPageWikiLink Robust_statistics.
- Standard_deviation wikiPageWikiLink Root-mean-square.