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If there are an even number of data points in the original ordered data set, split this data set exactly in half. 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.
It is defined as the difference between the 75th and 25th percentiles of the data. [2] [3] [4] To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. [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).
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 25th percentile is also known as the first quartile (Q 1), the 50th percentile as the median or second quartile (Q 2), and the 75th percentile as the third quartile (Q 3). For example, the 50th percentile (median) is the score below (or at or below, depending on the definition) which 50% of the scores in the distribution are found.
The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles. The use of the term "hinge" for the lower or upper quartiles derives from John Tukey 's work on exploratory data analysis in the late 1970s, [ 1 ] and "midhinge" is a fairly modern term dating from around that time.
A box plot of the data set can be generated by first calculating five relevant values of this data set: minimum, maximum, median (Q 2), first quartile (Q 1), and third quartile (Q 3). The minimum is the smallest number of the data set. In this case, the minimum recorded day temperature is 57°F. The maximum is the largest number of the data set.
upper whisker top end The middle three values – the lower quartile , median , and upper quartile – are the usual statistics from the five-number summary and are the standard values for the box in a box plot .
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.