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The QUARTILE function is a legacy function from Excel 2007 or earlier, giving the same output of the function QUARTILE.INC. In the function, array is the dataset of numbers that is being analyzed and quart is any of the following 5 values depending on which quartile is being calculated. [8]
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.
If data are placed in order, then the lower quartile is central to the lower half of the data and the upper quartile is central to the upper half of the data. These quartiles are used to calculate the interquartile range, which helps to describe the spread of the data, and determine whether or not any data points are outliers.
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In statistics, a k-th percentile, also known as percentile score or centile, is a score (e.g., a data point) below which a given percentage k of arranged scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage falls ("inclusive" definition); i.e. a score in the k-th percentile would be above approximately k% of all scores in its set.
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q 3 and Q 1. Each quartile is a median [8] calculated as follows. Given an even 2n or odd 2n+1 number of values first quartile Q 1 = median of the n smallest values third quartile Q 3 = median of the n largest values [8]
The quantile function, Q, of a probability distribution is the inverse of its cumulative distribution function F. The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function.
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.