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<h2 id="examples">Examples</h2> <p>Some examples of statistics are: </p> <ul><li>"In a recent survey of Americans, 52% of women say global warming is happening."</li></ul> <p>In this case, "52%" is a statistic, namely the percentage of women in the survey sample who believe in global warming. The population is the <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of all women in the United States, and the population parameter being estimated is the percentage of <i>all</i> women in the United States, not just those surveyed, who believe in global warming. </p> <ul><li>"The manager of a large hotel located near Disney World indicated that 20 selected guests had a mean length of stay equal to 5.6 days."</li></ul> <p>In this example, "5.6 days" is a statistic, namely the mean length of stay for our sample of 20 hotel guests. The population is the set of all guests of this hotel, and the population parameter being estimated is the mean length of stay for <i>all</i> guests.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> Whether the estimator is unbiased in this case depends upon the sample selection process; see <a href="/facts/Renewal_theory/1rDc2czB">the inspection paradox</a>. </p><p>There are a variety of functions that are used to calculate statistics. Some include: </p> <ul><li><a href="/facts/Sample_mean/Ah8VVVDT">Sample mean</a>, <a href="/facts/Sample_median/YwXGWTyr">sample median</a>, and <a href="/facts/Mode_(statistics)/vq5tGp0G">sample mode</a></li> <li><a href="/facts/Sample_variance/ULBJKXD1">Sample variance</a> and sample <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a></li> <li>Sample <a href="/facts/Quantile/oWr1MC3s">quantiles</a> besides the <a href="/facts/Median/YwXGWTyr">median</a>, e.g., <a href="/facts/Quartile/XLlNsqEP">quartiles</a> and <a href="/facts/Percentile/YKD2SDsw">percentiles</a></li> <li><a href="/facts/Test_statistic/IBwfN5Kx">Test statistics</a>, such as <a href="/facts/T-statistic/eTlyuoqG">t-statistic</a>, <a href="/facts/Chi-squared_statistic/EbjRpLJP">chi-squared statistic</a>, <a href="/facts/F-test/Kq8lzNqY">f statistic</a></li> <li><a href="/facts/Order_statistic/QS3RnGcC">Order statistics</a>, including sample maximum and minimum</li> <li>Sample <a href="/facts/Moment_(mathematics)/GL7vJ1nb">moments</a> and functions thereof, including <a href="/facts/Kurtosis/yqGgry89">kurtosis</a> and <a href="/facts/Skewness/rdS8luFa">skewness</a></li> <li>Various <a href="/facts/Functional_(mathematics)/3Cp3PHBR">functionals</a> of the <a href="/facts/Empirical_distribution_function/frWIF9F9">empirical distribution function</a></li></ul> <h2 id="properties">Properties</h2> <h3>Observability</h3> <p>Statisticians often contemplate a <a href="/facts/Parameterized_family/YoEWw0I8">parameterized family</a> of <a href="/facts/Probability_distribution/EpsKKVRu">probability distributions</a>, any member of which could be the distribution of some measurable aspect of each member of a population, from which a sample is drawn randomly. For example, the parameter may be the average height of 25-year-old men in North America. The height of the members of a sample of 100 such men are measured; the average of those 100 numbers is a statistic. The average of the heights of all members of the population is not a statistic unless that has somehow also been ascertained (such as by measuring every member of the population). The average height that would be calculated using <i>all</i> of the individual heights of <i>all</i> 25-year-old North American men is a parameter, and not a statistic. </p> <h3>Statistical properties</h3> <p>Important potential properties of statistics include <a href="/facts/Completeness_(statistics)/pkF2PzCL">completeness</a>, <a href="/facts/Consistent_estimator/HAKDWYEM">consistency</a>, <a href="/facts/Sufficiency_(statistics)/eClRXHpd">sufficiency</a>, <a href="/facts/Estimator_bias/oxIvEgmd">unbiasedness</a>, <a href="/facts/Minimum_mean_square_error/hI2lqEMh">minimum mean square error</a>, low <a href="/facts/Variance/ULBJKXD1">variance</a>, <a href="/facts/Robust_statistics/RwIMvtD2">robustness</a>, and computational convenience. </p> <h3>Information of a statistic</h3> <p>Information of a statistic on model parameters can be defined in several ways. The most common is the <a href="/facts/Fisher_information/Q2JLexN9">Fisher information</a>, which is defined on the statistic model induced by the statistic. <a href="/facts/Kullback_information/nh7SjlPE">Kullback information</a> measure can also be used. </p> <h2 id="see-also">See also</h2> Look up <i>statistic</i> in Wiktionary, the free dictionary. <ul><li><a href="/facts/Statistics/DNPsKGYU">Statistics</a></li> <li><a href="/facts/Statistical_theory/7s5ye1mp">Statistical theory</a></li> <li><a href="/facts/Descriptive_statistics/vnTP8Ryr">Descriptive statistics</a></li> <li><a href="/facts/Statistical_hypothesis_testing/yv9RPF6U">Statistical hypothesis testing</a></li> <li><a href="/facts/Summary_statistic/o213eGso">Summary statistic</a></li> <li><a href="/facts/Well-behaved_statistic/mNL9zjS8">Well-behaved statistic</a></li></ul> <ul><li>Kokoska, Stephen (2015). <i>Introductory Statistics: A Problem-Solving Approach</i> (2nd ed.). New York: W. H. Freeman and Company. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4641-1169-3.</li> <li>Parker, Sybil P (editor in chief). "Statistic". McGraw-Hill Dictionary of Scientific and Technical Terms. Fifth Edition. McGraw-Hill, Inc. 1994. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-07-042333-4. Page 1912.</li> <li>DeGroot and Schervish. "Definition of a Statistic". Probability and Statistics. International Edition. Third Edition. Addison Wesley. 2002. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-321-20473-5. Pages 370 to 371.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Kokoska 2015, p. 296-308. - Kokoska, Stephen (2015). Introductory Statistics: A Problem-Solving Approach (2nd ed.). New York: W. H. Freeman and Company. ISBN 978-1-4641-1169-3. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Kokoska 2015, p. 296-297. - Kokoska, Stephen (2015). Introductory Statistics: A Problem-Solving Approach (2nd ed.). New York: W. H. Freeman and Company. ISBN 978-1-4641-1169-3. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> </ol>