3.9 Quantiles
In general, we can view quantiles as positional measures that divide the observations on a variable X into a number of equal portions (given that the data values are in an increasing sequence). We have already encountered the median of a data set; it is a positional value that splits the data into two equal parts. Others are:
There are three computed quartiles that will divide the observations on a variable X into four equal parts: Q1, Q2, and Q3. In this regard, 25% of all observations on X lie below Q1; 50% of all observations on X lie below Q2 ( = median); and 75% of all observations on X lie below Q3. Remember that quartiles are “positional values.” Hence the following:
(3.12b)
(3.12c)
(provided, of course, that our data have been arranged in an increasing sequence). Given Equation (3.12), we can easily calculate the interquartile range (IQR) as IQR = Q3 − Q1—it is the range between the first and third quartiles and serves to locate the middle 50% of the observations on a variable X. Then the quartile deviation ...
Get Statistical Inference: A Short Course now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.