The first quartile (Q 1), also known as the "small quartile", is equal to the 25th percentile of all values in descending order in the sample.
The second quartile (Q2), also known as the "median", is equal to the 50th percentile of all values in the sample in descending order.
The third quartile (Q3), also known as the "larger quartile", is equal to the 75th percentile of all values in descending order in the sample.
The gap between the third quartile and the first quartile is also called quartile spacing (IQR).
Extended data:
For a finite set of numbers, we can sort all the observed values and find the middle one as the median. If there are even numbers of observations, the median is not unique, and the average of the two intermediate values is usually taken as the median, that is, dichotomy.
At most, half of the values in a data set are less than the median, and at most, half of the values are greater than the median. If the number of values greater than and less than the median is less than half, there must be some values in the set equal to the median.
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