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The interquartile range (IQR) is a measure of spread in statistics. The observations (data) are arranged in order of magnitude - usually smallest to largest.

Suppose there are n observations. Then calculate (n+1)/4 and round it to m, say. For large n (>30) don't bother with the +1 Then find the values of the observations is positions m and 3m. [That last sentence would be so much simpler if this crap browser allowed superscripts but mth and 3mth is confusing!] The number in position m is called the "Lower Quartile" and a quarter of the observations are smaller than it is. The number in position 3m is called the "Upper Quartile" and a quarter of the observations are greater than it is. The difference between the two values (not m and 3m but the values of the observations in those positions) is the IQR.


Since a quarter of the observations are smaller than the LQ and a quarter are larger than the UQ, the IQR contains the middle half of all observations.


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Q: What is the interquartile range in math?
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