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The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data. This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions.
These quartiles are denoted by Q 1 (also called the lower quartile), Q 2 (the median), and Q 3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q 3 − Q 1 [1]. The IQR is an example of a trimmed estimator, defined as the 25% trimmed ...
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)
The third quartile value for the original example above is determined by 11×(3/4) = 8.25, which rounds up to 9. The ninth value in the population is 15. 15 Fourth quartile Although not universally accepted, one can also speak of the fourth quartile. This is the maximum value of the set, so the fourth quartile in this example would be 20.
Box plot of data from the Michelson experiment. In descriptive statistics, a box plot or boxplot is a method for demonstrating graphically the locality, spread and skewness groups of numerical data through their quartiles. [1] In addition to the box on a box plot, there can be lines (which are called whiskers) extending from the box indicating ...
The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function. The quantile function, Q, of a probability distribution is the inverse of its cumulative ...
The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range. The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining scores.
Seven-number summary. In 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 ...