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The first quartile (Q 1) is defined as the 25th percentile where lowest 25% data is below this point. It is also known as the lower quartile. The second quartile (Q 2) is the median of a data set; thus 50% of the data lies below this point. The third quartile (Q 3) is the 75th percentile where lowest 75% data is below this point.
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 ...
Splitting the observations either side of the median gives two groups of four observations. The median of the first group is the lower or first quartile, and is equal to (0 + 1)/2 = 0.5. The median of the second group is the upper or third quartile, and is equal to (27 + 61)/2 = 44. The smallest and largest observations are 0 and 63.
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.
It follows that the median is , the lower quartile is / and the upper quartile ... From Euler's reflection formula, the expression can be simplified further: ...
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.
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.
In statistics, the quartile coefficient of dispersion (QCD) is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation .