In descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information 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 mean absolute 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
Entries in an analysis of variance table can also be regarded as summary statistics.
Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation, mean absolute difference and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation.
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.
Human Perception of Summary Statistics
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- Piazza, Elise A.; Sweeny, Timothy D.; Wessel, David; Silver, Michael A.; Whitney, David (2013). "Humans Use Summary Statistics to Perceive Auditory Sequences". Psychological Science. 24 (8): 1389–1397. doi:10.1177/0956797612473759. PMC 4381997. PMID 23761928.
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- Utochkin, Igor S. (2015). "Ensemble summary statistics as a basis for rapid visual categorization". Journal of Vision. 15 (4): 8. doi:10.1167/15.4.8. PMID 26317396.
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