Sample (statistics)

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A sample is that part of a population which is actually observed. In normal scientific practice, we demand that it is selected in such a way as to avoid presenting a biased view of the population. If statistical inference is to be used, there must be a way of assigning known probabilities of selection to each sample. If the probabilities of different samples are all equal, for example, the method is called simple random sampling.

In mathematical terms, given a random variable X with distribution F, a sample of length <math>n\in\mathbb{N}</math> is a set of <math>n</math> independent, identically distributed (iid) random variables with distribution F. It concretely represents n experiments in which we measure the same quantity. For example, if X represents the height of an individual and we measure <math>n</math> individuals, <math>X_i</math> will be the height of the i-th individual. Note that a sample of random variables (i.e. a set of measurable functions) most not be confused with the realisations of these variables (which are the values that these random variables take). In other words, <math>X_i</math> is a function representing the mesure at the i-th experiment and <math>x_i=X_i(\omega)</math> is the value we actually get when making the measure.

See also: Sampling (statistics)

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