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How to find data quantile by dichotomy?
The calculation method of 75% quantile in senior high school mathematics is as follows:

75% quantile, that is, first sort the data from small to large, then calculate the sample size n multiplied by 75% to get a number m, and then look at the sorted m-th wheat. 75% quantile means that 75% of the data is less than or equal to this number (that is, 75% quantile) and 25% is greater than or equal to this number.

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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.

The way to calculate the quantile of a limited number of data is to arrange all the data of the same kind in order of size. If the number of data is odd, the middle data is the median of this group of data; If the number of data is even, the arithmetic mean of the middle two data is the median of this set of data.