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Learn how to calculate and interpret the range of a set of data, a measure of dispersion that is the difference between the largest and smallest values. Find out the distribution, moments, and related quantities of the range for continuous and discrete random variables.
Learn the definition, notation, examples, and probabilistic analysis of order statistics, which are the k th-smallest values of a statistical sample. Find out how order statistics are related to the uniform, exponential, and Erlang distributions.
The interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. It is defined as the difference between the 75th and 25th percentiles of the data, and can be used to build box plots, identify outliers, and test normality.
Learn about the concept and measures of statistical dispersion, which is the extent to which a distribution is stretched or squeezed. Compare different types of dispersion measures, such as standard deviation, interquartile range, and entropy, and their applications in various fields.
A quartile is a quantile that divides a data set into four equal parts. The first quartile (Q1) is the 25th percentile, the second quartile (Q2) is the median, and the third quartile (Q3) is the 75th percentile. Learn how to compute quartiles for discrete and continuous distributions.
Dixon's Q test is a statistical method to detect and remove outliers from a data set assuming normal distribution. It calculates Q as the absolute difference between the outlier and the closest value, and compares it with a reference value from a table based on sample size and confidence level.
A confidence interval is an interval that is expected to contain a parameter being estimated with a certain probability. Learn how to construct and interpret confidence intervals for different parameters and distributions, and how they relate to hypothesis testing and bootstrapping.
A probability density function (PDF) is a function that provides a relative likelihood of a continuous random variable taking a value. Learn the definition, examples, properties and applications of PDFs in probability theory and statistics.