How Do I Calculate the Upper or Lower Quartile?
To find the first quartile of a set of numbers, find the median of the lowest half of the data set. This median is the first, or lowest, quartile in the data set. To find the third, or upper, quartile of a data set, instead find the median of the higher half of numbers in the set.
Quartiles divide a set of numbers into four equal parts. To find the highest and lowest quartiles in a data set, first find the median of the entire set of numbers. Treat the sets of numbers above and below the median as separate sets, and then locate the medians of these groups. The median of the lowest set of numbers corresponds to the lowest, or first, quartile. The median of the entire set corresponds to the second quartile, whereas the median of the highest set corresponds to the highest, or third, quartile.
Quartiles are calculated differently for odd and even numbers of values. If a data set has an odd number of digits, the median is the middle value. If a data set has an even number of digits, the median is the average of the middle two numbers. To find this average, add the two middle numbers together, and then divide the sum by two.