Quartiles
A Quartile is a percentile measure that divides the total of into four equal parts: . A particular quartile is the border between two neighboring quarters of the distribution.
(quartile ) separates the bottom of the ranked data (Data is ranked when it is arranged in order.) from the top . (quartile ) is the mean or average. (quartile ) separates the top of the ranked data from the bottom . More precisely, at least of the data will be less than or equal to and at least will be greater than or equal . At least of the data will be less than or equal to while at least of the data will be greater than or equal to .
Example 1:
Find the quartile, median, and quartile of the following set of data.
There are numbers in the data set, already arranged from least to greatest. The number, , is the middle value. So is the median.
Once we remove , the lower half of the data set is
Here, the middle number is . So, .
The top half of the data set is
Here, the middle number is . So, .
The interquartile range or IQR is the distance between the first and third quartiles. It is sometimes called the H-spread and is a stable measure of disbursement. It is obtained by evaluating .