Quartiles
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The quartiles are three values which divide the sorted data set into four (approximately) equal parts. We cannot divide a set of 17 (say) data values into four equal parts since that would require splitting a datum. What we can do is interpolate between data items which bracket the desired position.
i x[i]
1 102
2 105
----------- the first quartile, Q[1]
3 106
4 109
------------ the second quartile or median or Q[2]
5 110
6 112
------------ the third quartile, Q[3]
7 115
8 118