Quartiles and interquartile range are among the measures of position. Just like the name indicates, quartiles divide a ranked data (ordered set of data ) into four equal parts. Only three measures are needed to divide any data set into four equal parts.
These three measures that will divide an ordered data set into four equal parts are the first quartile (denoted by Q_{1}), the second quartile (denoted by Q_{2}), and the third quartile (denoted by Q_{3}).
After a data set has been ordered, or written in increasing order, here is how we define the quartiles.
The second quartile or Q_{2}_{ }is the same as the median of the data set after the set has been ordered.
The first quartile or Q_{1 }is the median between the smallest number and the second quartile.
The third quartile or Q_{3} is the median between the second quartile and the biggest number.
Now, take a look at the following figure and then make the following important observations.
The interquartile range is the difference between third quartile and the first quartile.
IQR = Interquartile range = Q_{3 }- Q_{1}
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