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First arrange the data set in ascending order.

Suppose the data set consists of n observations.

the index for the lower quartile is (n + 1)/4

and the index for the upper quartile is 3*(n + 1)/4.

Find the values that correspond to the number in these positions in the ordered list.

For example, if n = 15, then lower index = 4 and upper index = 12.

So the lower quartile is the fourth number and the upper quartile is the twelfth.

If n is large, you may skip the +1 and just look at n/4 and 3n/4.

Often the indices are not integers. Then, if you are a beginner (nd the fact that you asked this question suggests that you are), find the nearest whole numbers for the two indices. Otherwise you need to interpolate and that is a whole new ball game!

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Q: How do you find the quartiles of a data set?
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