### You can’t take medians and add, subtract, or divide them

You have a report that gives for each industry the median number of litigation cases per law department in the industry.  Let’s say 45 cases.  A later table in the report gives medians for subsets of that total number, such as medians of employment cases (perhaps 12), of patent cases (3), and of all other cases (28).

What you should not do is add up the individual case-type medians (12+3+28 = 43) and expect the sum to be the same as the median number of total litigation cases (45).  The reason is that each median stands on its own and was created on its own.  The software sorts each one high to low and picks the middle value.  It would be merely a coincidence if the sorted list of total number of cases arrived at the same number.

One reason is that if the sorted list has an even number of items, the software averages the middle two – a figure that the other lists, if they have odd integers of items, will never produce.  A second reason is that one or more of the component lists (employment, patent and other in the example) might have some missing data, which would throw off a potential match of medians.