In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount as simply as possible. Statisticians commonly try to describe the observations in
- a measure of location, or central tendency, such as the arithmetic mean
- a measure of statistical dispersion like the standard deviation
- a measure of the shape of the distribution like skewness or kurtosis
- if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient
> x <- rnorm(n=50, mean=0, sd=1) > summary(x) Min. 1st Qu. Median Mean 3rd Qu. Max. -1.72700 -0.49650 -0.05157 0.07981 0.67640 2.46700
Examples of summary statistics
Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation.
The Gini coefficient was originally developed to measure income inequality and is equivalent to one of the L-moments.
Common measures of the shape of a distribution are skewness or kurtosis, while alternatives can be based on L-moments. A different measure is the Distance skewness, for which a value of zero implies central symmetry.
A simple summary of a dataset is sometimes given by quoting particular order statistics as approximations to selected percentiles of a distribution.
The common measure of dependence between paired random variables is the Pearson product-moment correlation coefficient, while a common alternative summary statistic is Spearman's rank correlation coefficient. Distance correlation equals zero implies independence.
Statistics Descriptive statisticsSummary tables Data collectionDesigning studiesUncontrolled studies Statistical inferenceFrequentist inferenceSpecific tests Correlation and regression analysisNon-standard predictorsPartition of variance Categorical, multivariate, time-series, or survival analysis Applications
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