Select term:
Statistics Dictionary Absolute Value Accuracy Addition Rule Alpha Alternative Hypothesis ANOVA Back-to-Back Stemplots Balanced Design Bar Chart Bartlett's Test Bayes Rule Bayes Theorem Bias Biased Estimate Bimodal Distribution Binomial Distribution Binomial Experiment Binomial Probability Binomial Random Variable Bivariate Data Blinding Blocking Blocking Variable Boxplot Cartesian Plane Categorical Variable Census Central Limit Theorem Chi-Square Distribution Chi-Square Goodness of Fit Test Chi-Square Statistic Chi-Square Test for Homogeneity Chi-Square Test for Independence Cluster Cluster Sampling Coefficient of Determination Coefficient of Multiple Determination Column Vector Combination Complement Completely Randomized Design Conditional Distribution Conditional Frequency Conditional Probability Confidence Interval Confidence Level Confounding Contingency Table Continuous Probability Distribution Continuous Variable Control Group Convenience Sample Correlation Covariance Critical Parameter Value Critical Value Cumulative Frequency Cumulative Frequency Plot Cumulative Probability Decision Rule Degrees of Freedom Dependent Variable Determinant Deviation Score Diagonal Matrix Discrete Probability Distribution Discrete Variable Discriminant Analysis Disjoint Disproportionate Stratification Dotplot Double Bar Chart Double Blinding Dummy Variable E Notation Echelon Matrix Effect Size Element Elementary Matrix Operations Elementary Operators Empty Set Epsilon Estimation Estimator Event Event Multiple Expected Value Experiment Experimental Design Extraneous Variable F Distribution F Statistic Factor Factorial Factorial Experiment Finite Population Correction Fixed Effects Model Fixed Factor Frequency Count Frequency Table Full Rank Gaps in Graphs Geometric Distribution Geometric Probability Hartley's Fmax Test Heterogeneous Histogram Homogeneous Hypergeometric Distribution Hypergeometric Experiment Hypergeometric Probability Hypergeometric Random Variable Hypothesis Test Identity Matrix Independent Independent Groups Design Independent Variable Influential Point Inner Product Interaction Plot Interactions Interquartile Range Intersection Interval Estimate Interval Scale Inverse IQR Joint Frequency Joint Probability Distribution Law of Large Numbers Level Line Linear Combination of Vectors Linear Dependence of Vectors Linear Transformation Logarithm Lurking Variable Margin of Error Marginal Distribution Marginal Frequency Marginal Mean Matched Pairs Design Matched-Pairs t-Test Matrix Matrix Dimension Matrix Inverse Matrix Order Matrix Rank Matrix Transpose Mauchly's Sphericity Test Mean Mean Square Measurement Scales Median Mixed Model Mode Multicollinearity Multinomial Distribution Multinomial Experiment Multiple Regression Multiplication Rule Multistage Sampling Mutually Exclusive Natural Logarithm Negative Binomial Distribution Negative Binomial Experiment Negative Binomial Probability Negative Binomial Random Variable Neyman Allocation Nominal Scale Nonlinear Transformation Non-Probability Sampling Nonresponse Bias Normal Distribution Normal Random Variable Null Hypothesis Null Set Observational Study One-Sample t-Test One-Sample z-Test One-stage Sampling One-Tailed Test One-Way ANOVA One-Way Table Optimum Allocation Ordinal Scale Outer Product Outlier Paired Data Parallel Boxplots Parameter Pearson Product-Moment Correlation Percentage Percentile Permutation Placebo Point Estimate Poisson Distribution Poisson Experiment Poisson Probability Poisson Random Variable Population Power Precision Probability Probability Density Function Probability Distribution Probability Sampling Proportion Proportionate Stratification P-Value Qualitative Variable Quantitative Variable Quartile Random Effects Model Random Factor Random Number Table Random Numbers Random Sampling Random Variable Randomization Randomized Block Design Randomized Block Experiment Range Ratio Scale Reduced Row Echelon Form Region of Acceptance Region of Rejection Regression Relative Frequency Relative Frequency Table Repeated Measures Design Replication Representative Residual Residual Plot Response Bias Row Echelon Form Row Vector Sample Sample Design Sample Point Sample Space Sample Survey Sampling Sampling Distribution Sampling Error Sampling Fraction Sampling Method Sampling With Replacement Sampling Without Replacement Scalar Matrix Scalar Multiple Scatterplot Selection Bias Set Significance Level Simple Random Sampling Simple Regression Singular Matrix Skewness Slope Sphericity Standard Deviation Standard Error Standard Normal Distribution Standard Score Statistic Statistical Experiment Statistical Hypothesis Statistics Stemplot Strata Stratified Sampling Subset Subtraction Rule Sum Vector Sums of Squares Symmetric Matrix Symmetry Systematic Sampling T Distribution T Score T Statistic Test Statistic Transpose Treatment t-Test Two-Sample t-Test Two-stage Sampling Two-Tailed Test Two-Way Table Type I Error Type II Error Unbiased Estimate Undercoverage Uniform Distribution Unimodal Distribution Union Univariate Data Variable Variance Variance Inflation Factor Vector Inner Product Vector Outer Product Vectors Venn Diagram Voluntary Response Bias Voluntary Sample Y Intercept z-score

Standard Deviation

The standard deviation is a numerical value used to indicate how widely individuals in a group vary. If individual observations vary greatly from the group mean, the standard deviation is big; and vice versa.

It is important to distinguish between the standard deviation of a population and the standard deviation of a sample. They have different notation, and they are computed differently. The standard deviation of a population is denoted by σ and the standard deviation of a sample, by s.

The standard deviation of a population is defined by the following formula:

σ = sqrt [ Σ ( X_i - X )² / N ]

where σ is the population standard deviation, X is the population mean, X_i is the ith element from the population, and N is the number of elements in the population.

The standard deviation of a sample is defined by slightly different formula:

s = sqrt [ Σ ( x_i - x )² / ( n - 1 ) ]

where s is the sample standard deviation, x is the sample mean, x_i is the ith element from the sample, and n is the number of elements in the sample.

And finally, the standard deviation is equal to the square root of the variance.

See also:

Statistics Tutorial: Measures of Variability | AP Statistics Tutorial: Measures of Variability | Random Variable Attributes