- Sample (statistics)
In

statistics , a**sample**is asubset of a population. Typically, the population is very large, making acensus or a completeenumeration of all the values in the population impractical or impossible. The sample represents a subset of manageable size. Samples are collected and statistics are calculated from the samples so that one can makeinference s orextrapolation s from the sample to the population. This process of collecting information from a sample is referred to as sampling.The best way to avoid a biased or unrepresentative sample is to select a

random sample , also known as a probability sample. A random sample is defined as a sample where theprobability that any individual member from the population being selected as part of the sample is exactly the same as any other individual member of the population. Several types of random samples aresimple random sample s, systematic samples, stratified random samples, and cluster random samples.A sample that is not random is called a

nonrandom sample or a nonprobability sample. Some examples of nonrandom samples areconvenience sample s,judgment sample s,purposive sample s,quota sample s, snowball samples, andquadrature node s inquasi-Monte Carlo method s.**Mathematical description of random sample**In mathematical terms, given a

random variable "X" with distribution "F", a random sample of length "n" =1,2,3,... is a set of "n" independent, identically distributed (iid) random variables with distribution "F". []Samuel S. Wilks , "Mathematical Statistics", John Wiley, 1962, Section 8.1A sample concretely represents "n" experiments in which we measure the same quantity. For example, if "X" represents the height of an individual and we measure $n$ individuals, $X\_i$ will be the height of the "i"-th individual. Note that a sample of random variables (i.e. a set of measurable functions) must not be confused with the realizations of these variables (which are the values that these random variables take). In other words, $X\_i$ is a function representing the measurement at the i-th experiment and $x\_i=X\_i(omega)$ is the value we actually get when making the measurement.

The concept of a sample thus includes the "process" of how the data are obtained (that is, the random variables). This is necessary so that mathematical statements can be made about the sample and

statistic s computed from it, such as thesample mean and covariance .**References****ee also***

Estimation theory

*Sampling (statistics)

*Sample size

*Multiset#Cumulant generating function **External links*** [

*http://www.socialresearchmethods.net/kb/sampstat.htm Statistical Terms Made Simple*]

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