# Find lower and upper quartiles of the data set. Interquartile range

Here we have a data set: 3, 5, 3, 4, 7, 8, 2, 3, 8, 2, 1, 5. Find lower and upper quartiles of this data set. Then calculate an interquartile range.

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First of all, we put the list of numbers in order: $$1,2,2,3,3,3,4,5,5,7,8,8$$ Then we cut the list of numbers into four equal parts: $$1,2,2,|\ 3,3,3,|\ 4,5,5,|\ 7,8,8$$ $$\text{Lower quartile }(Q_1)=\frac{2+3}{2}=2.5$$ $$\text{Upper quartile }(Q_3)=\frac{5+7}{2}=6$$ $$\text{Interquartile Range }(Q_3-Q_1)=6-2.5=3.5$$

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