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Quartiles

A Quartile is a percentile measure that divides the total of 100 % into four equal parts: 25 % , 50 % , 75 % and 100 % .  A particular quartile is the border between two neighboring quarters of the distribution.

  Q 1 (quartile 1 ) separates the bottom 25 % of the ranked data (Data is ranked when it is arranged in order.) from the top 75 % Q 2 (quartile 2 ) is the mean or average.  Q 3 (quartile 3 ) separates the top 25 % of the ranked data from the bottom 75 % .  More precisely, at least 25 % of the data will be less than or equal to Q 1 and at least 75 % will be greater than or equal Q 1 .  At least 75 % of the data will be less than or equal to Q 3 while at least 25 % of the data will be greater than or equal to Q 3 .

Example 1:

Find the 1 st quartile, median, and 3 rd quartile of the following set of data.

24 , 26 , 29 , 35 , 48 , 72 , 150 , 161 , 181 , 183 , 183

There are 11 numbers in the data set, already arranged from least to greatest. The 6 th number, 72 , is the middle value. So 72 is the median.

Once we remove 72 , the lower half of the data set is

24 , 26 , 29 , 35 , 48

Here, the middle number is 29 . So, Q 1 = 29 .

The top half of the data set is

150 , 161 , 181 , 183 , 183

Here, the middle number is 181 . So, Q 3 = 181 .

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 Q 3 Q 1 .