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In descriptive statistics, the range of a set of data is size of the narrowest interval which contains all the data. It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical ...
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered.
The sample range is the difference between the maximum and minimum. It is a function of the order statistics: {, …,} = (). A similar important statistic in exploratory data analysis that is simply related to the order statistics is the sample interquartile range.
This can be generalized to restrict the range of values in the dataset between any arbitrary points and , using for example ′ = + (). Note that some other ratios, such as the variance-to-mean ratio ( σ 2 μ ) {\textstyle \left({\frac {\sigma ^{2}}{\mu }}\right)} , are also done for normalization, but are not nondimensional: the units do not ...
The data shown is a random sample of 10,000 points from a normal distribution with a mean of 0 and a standard deviation of 1. The data used to construct a histogram are generated via a function m i that counts the number of observations that fall into each of the disjoint categories (known as bins).
Common measures of statistical dispersion are the standard deviation, variance, range, interquartile range, absolute deviation, mean absolute difference and the distance standard deviation. Measures that assess spread in comparison to the typical size of data values include the coefficient of variation .
Data may be collected, presented and summarised, in one of two methods called descriptive statistics. Two elementary summaries of data, singularly called a statistic, are the mean and dispersion. Whereas inferential statistics interprets data from a population sample to induce statements and predictions about a population. [6] [7] [5]
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.