A quantile is a value at or below which a stated fraction of the data lies. Some examples of quantiles include:
The formula for the position of a percentile in a data set with n observations sorted in ascending order is:
Ly = (n+1) y /100
Calculate the first quartile of a distribution that consists of the following portfolio returns:
3%, 4%, 6%, 9%, 11%, 12%, 14%
Solution:
The first quartile = (7+1) 25/100 = 2nd item in the data set (4%). i.e. 25% of the observations lie below the second observations from the left.
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