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
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.
A simple summary of a dataset is sometimes given by quoting particular order statistics as approximations to selected percentiles of a distribution.
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.
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. A value of zero for the distance correlation implies independence.
Human perception of summary statistics
- Upton, Graham; Cook, Ian (2008-10-02). "Dictionary (S)" (in en-gb). A Dictionary of Statistics (Second (revised) ed.). Oxford University Press. ISBN 978-0199541454. OCLC 935100347. https://archive.org/details/dictionaryofstat0000upto/page/378/mode/1up. "summary statistics [...] *ANOVA table might be referred to as summary statistics"
- Bullen, P. S. (2003-08-31) (in en). Handbook of Means and Their Inequalities. Mathematics and Its Applications. 560 (2 ed.). Springer Dordrecht. doi:10.1007/978-94-017-0399-4. ISBN 978-1-4020-1522-9. OCLC 939214285.
- Grabisch, Michel; Marichal, Jean-Luc; Mesiar, Radko; Pap, Endre (2009). Aggregation Functions. Oxford University Press. ISBN 978-0521519267.
- 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. PMID 23761928.
- Alexander, R. G.; Schmidt, J.; Zelinsky, G. Z. (2014). "Are summary statistics enough? Evidence for the importance of shape in guiding visual search.". Visual Cognition 22 (3–4): 595–609. doi:10.1080/13506285.2014.890989. PMID 26180505.
- 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.
Original source: https://en.wikipedia.org/wiki/Summary statistics. Read more