The IQR describes the middle 50% of values when ordered from lowest to highest.
Given a dataset, to find the interquartile range first find the median (middle value) of the lower(first quartile) and upper half of the data(third quartile), and then find their difference.
Our dataset is
[tex]\lbrace0,0,0,2,3,4,7,7,8,12,14,15,15,16,18\rbrace[/tex]We have 15 elements on this dataset. The median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. Since we have 15 elements, the middle element is the 8th element(this way we have 7 elements below and 7 elements above our median). The 7 elements below are
[tex]\lbrace0,0,0,2,3,4,7\rbrace[/tex]The median of those points are the first quartile. The median of this dataset is 2.
For the upper half of the data, we have
[tex]\lbrace8,12,14,15,15,16,18\rbrace[/tex]The median is 15, therefore, the third quartile is 15.
The interquartile range is the difference between those values.
[tex]15-2=13[/tex]The IQR of our dataset is 13.
