Statistique d'ordreEn statistiques, la statistique d'ordre de rang k d'un échantillon statistique est égal à la k-ième plus petite valeur. Associée aux statistiques de rang, la statistique d'ordre fait partie des outils fondamentaux de la statistique non paramétrique et de l'inférence statistique. Deux cas importants de la statistique d'ordre sont les statistiques du minimum et du maximum, et dans une moindre mesure la médiane de l'échantillon ainsi que les différents quantiles.
Quartilevignette|Histogramme avec représentation visuelle des quartiles. En statistique descriptive, un quartile est chacune des trois valeurs qui divisent les données triées en quatre parts égales, de sorte que chaque partie représente 1/4 de l'échantillon de population. Le quartile fait partie des quantiles.
Range (statistics)In statistics, the range of a set of data is the difference between the largest and smallest values, the result of subtracting the sample maximum and minimum. It is expressed in the same units as the data. In descriptive statistics, range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. Since it only depends on two of the observations, it is most useful in representing the dispersion of small data sets.
Five-number summaryThe 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) In addition to the median of a single set of data there are two related statistics called the upper and lower quartiles.
Sample maximum and minimumIn statistics, the sample maximum and sample minimum, also called the largest observation and smallest observation, are the values of the greatest and least elements of a sample. They are basic summary statistics, used in descriptive statistics such as the five-number summary and Bowley's seven-figure summary and the associated box plot. The minimum and the maximum value are the first and last order statistics (often denoted X(1) and X(n) respectively, for a sample size of n).
Summary statisticsIn descriptive statistics, summary statistics are used to summarize a set of observations, in order to communicate the largest amount of information as simply as possible. Statisticians commonly try to describe the observations in a measure of location, or central tendency, such as the arithmetic mean a measure of statistical dispersion like the standard mean absolute deviation a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot.
L-estimatorIn statistics, an L-estimator is an estimator which is a linear combination of order statistics of the measurements (which is also called an L-statistic). This can be as little as a single point, as in the median (of an odd number of values), or as many as all points, as in the mean. The main benefits of L-estimators are that they are often extremely simple, and often robust statistics: assuming sorted data, they are very easy to calculate and interpret, and are often resistant to outliers.
Seven-number summaryIn descriptive statistics, the seven-number summary is a collection of seven summary statistics, and is an extension of the five-number summary. There are three similar, common forms. As with the five-number summary, it can be represented by a modified box plot, adding hatch-marks on the "whiskers" for two of the additional numbers. The following percentiles are (approximately) evenly spaced under a normally distributed variable: the 2nd percentile (better: 2.15%) the 9th percentile (better: 8.
Exploratory data analysisIn statistics, exploratory data analysis (EDA) is an approach of analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling and thereby contrasts traditional hypothesis testing. Exploratory data analysis has been promoted by John Tukey since 1970 to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments.
MidhingeIn statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location. Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. The midhinge is related to the interquartile range (IQR), the difference of the third and first quartiles (i.e. ), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles.
