![]() The median, minimum, maximum, and the first and third quartile constitute the Five-number summary. This means the 1.5*IQR whiskers can be uneven in lengths. Pattern of latter two bullet points: If there are no data points at the true quartiles, use data points slightly "inland" (closer to the median) from the actual quartiles.(If there is no data point at 12, then the highest point less than 12.) (If there is no data point at 4, then the lowest point greater than 4.) Interquartile range, IQR = Q 3 - Q 1 = 2.The following table has 13 rows, and follows the rules for the odd number of entries.įor the data in this table the interquartile range is IQR = Q 3 − Q 1 = 119 - 31 = 88.ĭata set in a plain-text box plot The second quartile Q 2 is the same as the ordinary median. Given an even 2n or odd 2n+1 number of valuesįirst quartile Q 1 = median of the n smallest values third quartile Q 3 = median of the n largest values Each quartile is a median calculated as follows. The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q 3 and Q 1. The quartile deviation or semi-interquartile range is defined as half the IQR. The IQR also may indicate the skewness of the dataset. The IQR can be used to identify outliers (see below). The median is the corresponding measure of central tendency. The IQR is used in businesses as a marker for their income rates.įor a symmetric distribution (where the median equals the midhinge, the average of the first and third quartiles), half the IQR equals the median absolute deviation (MAD). The IQR is used to build box plots, simple graphical representations of a probability distribution. Unlike total range, the interquartile range has a breakdown point of 25%, and is thus often preferred to the total range. ![]() It is also used as a robust measure of scale It can be clearly visualized by the box on a box plot. The IQR is an example of a trimmed estimator, defined as the 25% trimmed range, which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q 3 − Q 1. These quartiles are denoted by Q 1 (also called the lower quartile), Q 2 (the median), and Q 3 (also called the upper quartile). To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. ![]() It is defined as the difference between the 75th and 25th percentiles of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. In descriptive statistics, the interquartile range ( IQR) is a measure of statistical dispersion, which is the spread of the data. JSTOR ( May 2012) ( Learn how and when to remove this template message)īoxplot (with an interquartile range) and a probability density function (pdf) of a Normal N(0,σ 2) Population.Unsourced material may be challenged and removed.įind sources: "Interquartile range" – news ![]() ![]() Please help improve this article by adding citations to reliable sources. This article needs additional citations for verification. ![]()
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