# Tutoring statistics, you talk about the median vs the mean. While the mean is probably used more (because of its involvement in the normal distribution), the median is preferred in some applications….

Back in my May 6 post, I briefly defined the mean and the median. In a student’s first couple of stats courses, the normal distribution (see my post here) is likely to dominate; it centres around the mean. So to a statistics student, the mean is likely the prominent measure of the “centre” of a set of data.

Real estate, however, might favour the median (at least, that’s my impression). I recall hearing the “median house price”, not the mean.

Why might the median be preferred to the mean? Let’s imagine the following numbers are prices of houses for sale in a small town:

Prices (K)

105 175 225 295 325

The list above, conveniently arranged in ascending order, has an obvious median value of 225K. Its mean is also 225K. The mean price and the median price of a house in this imaginary town are both 225K.

Now, let’s imagine the house at $325K sells. At the same time, a local millionaire decides to move, so puts his shack on the market, asking a million five hundred thousand. Let’s look at our new price list:

Prices (K)

105 175 225 295 1500

The median price remains 225K; the middle value in the list hasn’t changed. However, the mean has ballooned to 460K. The mean, of course, is the sum of the prices, divided by how many there are (five, in this case). Since 1500 is much higher than the number it replaced, the sum of the prices has dramatically increased; so, then, must the mean. After all, the number of houses for sale hasn’t changed.

A realtor in that town knows that if you hear its mean house price is 460K, you’re only likely to look at its listings if you’re rich. A first-time or middle-income buyer won’t likely be able to get a mortgage in the neighbourhood of 400K. Ironically, most houses in that town are very reasonably priced; only one in five is above 300K. In fact, first time and middle income buyers should be attracted to the town; the majority of its housing inventory is priced under 250K – distantly below the 460K average value. (*Mean* is the more refined term for *average*, from many people’s point of view).

The realtor decides that, in fact, the mean house price of 460K is misleading. While it’s academically true, it sends the message that the town is expensive to buy in. With 60% of its housing inventory below 250K – and 40% even below 200K – the town is actually a very affordable place to seek housing.

The realtor decides that the median house price of 225K reflects much better the affordability of housing in the town. Two houses are more, while two are less. The millionaire’s $1.5 million house won’t be of interest to most buyers, anyway.

The mean is potentially very sensitive to single values that are widely different from the general population. The median, by contrast, is much more stable in the face of atypical values. Therefore, some data consumers prefer the median to the mean.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.