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Boxplot (with an interquartile range) and a probability density function (pdf) of a Normal N (0,σ2) Population. In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [ 1 ] The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread.
IQR and MAD. One of the most common robust measures of scale is the interquartile range (IQR), the difference between the 75th percentile and the 25th percentile of a sample; this is the 25% trimmed range, an example of an L-estimator. Other trimmed ranges, such as the interdecile range (10% trimmed range) can also be used.
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 ...
v. t. e. Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other quantiles) of the response variable. [There is ...
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: the sample minimum (smallest observation) the lower quartile or first quartile. the median (the middle value) the upper quartile or third quartile. the sample maximum (largest observation)
A pivotal quantity is a function of data, whose underlying population distribution is a member of a parametric family, that is not dependent on the values of the parameters. An ancillary statistic is such a function that is also a statistic, meaning that it is computed in terms of the data alone. Such functions are robust to parameters in the ...
Another proposed solution was S-estimation. This method finds a line (plane or hyperplane) that minimizes a robust estimate of the scale (from which the method gets the S in its name) of the residuals. This method is highly resistant to leverage points and is robust to outliers in the response. However, this method was also found to be inefficient.
Quantile. Probability density of a normal distribution, with quantiles shown. The area below the red curve is the same in the intervals (−∞,Q1), (Q1,Q2), (Q2,Q3), and (Q3,+∞). In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or ...