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the sum of the upper quartile and lower quartile is 56 and their difference is 24. find upper quartile and lower quartile.
The interquartile range is the difference between the Lower quartile and the upper quartile. Obviously you need to be able to find these values. Haylock (2006) explains how to do this for difficult size groups in mathematics explained for primary teachers. He explains the position of the lower quartile is a quarter of (n+1) and that of the upper quartile is three-quarters of (n+1). So for a group of 7 numbers, you find a quarter of 8, which is 2. Therefore the number in second place is the lower quartile. Three quarters of 8 is 6 and so the number in 6th position is the upper quartile. Now take the lower quartile from the upper quartile.
you do work out the upper and lower quartile
You arrange the data set in ascending order. You then find the observation such that a quarter of the observations are smaller than it and three quarters are bigger. That value is the lower quartile. Next find the observation such that three quarters of the observations are smaller than it and a quarter are bigger. That value is the upper quartile. Upper quartile minus lower quartile = IQR.
It is the upper quartile minus the lower quartile.