Astatistic (singular) orsample statistic is any quantity computed from values in asample which is considered for a statistical purpose. Statistical purposes includeestimating apopulation parameter, describing a sample, or evaluating a hypothesis. Theaverage (or mean) of sample values is a statistic. The term statistic is used both for the function (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result of the average calculation). When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose.
When a statistic is used for estimating a population parameter, the statistic is called anestimator. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, thesample mean is anunbiased estimator of thepopulation mean. This means that theexpected value of the sample mean equals the true population mean.[1]
Adescriptive statistic is used to summarize the sample data. Atest statistic is used instatistical hypothesis testing. A single statistic can be used for multiple purposes – for example, the sample mean can be used to estimate the population mean, to describe a sample data set, or to test a hypothesis.
Some examples of statistics are:
In this case, "52%" is a statistic, namely the percentage of women in the survey sample who believe in global warming. The population is theset of all women in the United States, and the population parameter being estimated is the percentage ofall women in the United States, not just those surveyed, who believe in global warming.
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 forall guests.[2] Whether the estimator is unbiased in this case depends upon the sample selection process; seethe inspection paradox.
There are a variety of functions that are used to calculate statistics. Some include:
Statisticians often contemplate aparameterized family ofprobability distributions, 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 usingall of the individual heights ofall 25-year-old North American men is a parameter, and not a statistic.
Important potential properties of statistics includecompleteness,consistency,sufficiency,unbiasedness,minimum mean square error, lowvariance,robustness, and computational convenience.
Information of a statistic on model parameters can be defined in several ways. The most common is theFisher information, which is defined on the statistic model induced by the statistic.Kullback information measure can also be used.
