Sample

In statistics, a data sample is a set of data collected from a statistical population by a defined procedure. Population denotes a set of similar items or events which is of interest for some question or experiment.
== Definition ==
In mathematical terms, given a probability distribution F, a random sample of length n (where n may be any positive integer) is a set of realizations of n independent, identically distributed () random variables with distribution F.
A sample concretely represents the results of n experiments in which the same quantity is measured. For example, if we want to estimate the average height of members of a particular population, we measure the heights of n individuals. Each measurement is drawn from the probability distribution F characterizing the population, so each measured height x_i is the realization of a random variable X_i with distribution F. Note that a set 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 obtained when making the measurement.
== Sample size ==
The determination of the sample size (the act of choosing the number of observations or replicates to include in a statistical sample) is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is determined based on the expense of data collection, and the need to have sufficient statistical power. Larger sample sizes generally lead to increased precision when estimating unknown parameters.
== WikiProject Statistics ==
For practical reasons, sample sizes within WikiProject Statistics are divided into four categories:
* Values should follow the official drop rates with very little deviation. Predictions will be exact.
* Significant deviations from official values almost surely indicate changes inside the game or wrong official values.
* Values usually follow the official drop rates. Predictions will be quite accurate.
* Significant deviations from official values often indicate changes inside the game or even wrong official values.
* Undocumented "hidden rules" can be regarded as proven.
* Values usually do not differ from official drop rates by more than 2 percent.
* Larger deviations may hint at undocumented rules.
* The "acceptable" status is the threshold for moving a box from the Candidates to the main section on Pro Kit Boxes with hidden rules. 
* Values can deviate from official drop rates by several percent. Predictions bear the risk of being highly inaccurate.
* Values for smaller sub-groups like Engine or Tech cards can deviate even more as one more item of this kind can change percentages by 10 or more percent.
* Boxes with a "critical" status that are suspected to have hidden rules can be included in the Candidates section on Pro Kit Boxes with hidden rules. 
Category:Statistics