Understanding the Difference Between the Mean and Median

Posted by on Jan 6, 2014 in Process Improvement | 0 comments

The other day I was listening to a reporter on CNN talk about the median price of an apartment in New York city.  The price was a staggering \$820,000.  During the discussion that followed he said something that made me cringe.  He stated that very high priced apartments, those over \$2 million dollars, were causing the median to be higher than it should be.  What he failed to realize is the median is the middle value in a set of data and not the mean of the data.

Here is an example I use that demonstrates the difference (I call it the Bill Gates affect).  Let’s say we have 20 people in a room and that the mean income of the group is \$60,000.  (See figure 1 below).  Out of the blue, Bill Gates walks into the room.  What happens to the mean income of the group if Bill is included?  The mean gets inflated due to Bill’s income and is much, much larger than \$60,000. (See figure 2).  We say the mean is sensitive to extreme values, in this case Bill’s income.  On the other hand, the median, being insensitive to extreme values, changes very little and is still close to the \$60,000.

We typically use the median when our data is skewed and tails to the right or left (fig. 2) and use the mean when our data fits a bell-shaped (normal) pattern (fig. 1).

Figure 1

Figure 2