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you do work out the upper and lower quartile
No. The IQR is found by finding the lower quartile, then the upper quartile. You then minus the lower quartile value from the upper quartile value (hence "interquartile"). This gives you the IQR.
It is the upper quartile minus the lower quartile.
lower extreme,upper extreme,upper quartile, lower quartile, and the median
The interquartile range :)