I got a great email today.

Tim,

I was over at your favorite site today and one of the posts made me think. It was about why the housing industry uses median instead of average home prices when reporting market data. I got to thinking about that and the examples they give are pretty compelling and I’m wondering if the numbers are really lower than reported. I wanted to get your thoughts.

Here is the link: http://housingpanic.blogspot.com/2007/05/is-median-best-way-to-understand-whats.html

Dave

To understand why median is correct when reporting the housing market data you have to understand a little about statistics. The “average” or more correctly the “arithmetic mean” is subject to skewing by large deviations in a small subset of the data under consideration.

Using Keith’s example:

Here’s 10 homes:

100,000
100,000
100,000
100,000
200,000
200,000
300,000
500,000
600,000
1,000,000

This gives a median of $200K and an average or arithmetic mean of $320,000.

Then his next is the 600K home goes to 400K and the 1M goes to 800K

Here’s 10 homes:

100,000
100,000
100,000
100,000
200,000
200,000
300,000
500,000
400,000
800,000

This gives a median of $200K and an average or arithmetic mean of $280,000.

He tries to give the impression that this is somehow significant and perhaps dishonest to report median instead of average or mean because the average shows a greater rate of change.

But, let’s talk a little about exactly why the median really is the more correct way to report this data. The primary reason is to reduce the amount of skewing and thrashing caused by extremely high or low prices of a relatively small number of sales in the area. Recently, a new all time record of $50,000,000 was paid for an apartment in New York City. No, not the building, just one single apartment. If we used the average to report the sales in that area it would show a large increase for one reporting period, but the median isn’t changed much by that one sale. Then in the next reporting period the average would be way down. Someone who doesn’t understand what they are looking at could conclude that housing prices are wildly unstable when in fact they are still trending down over all the reporting periods under consideration in that area.
The median sale price in any given area doesn’t tell us much as a number, but how it changes over time is very important to investors. If the median price is moving up then it tells me there is more demand on the higher side of the market, if it is moving down, it tells me the demand is there. To an investor that is far more important than the average sale price in an area.

To add to the confusion, misinformed Realtors will often report average sales prices for a neighborhood and while the delta between the two metrics may not be that much within a monolithic neighborhood it can vary wildly in mixed neighborhoods.

Looking at how the median changes over time is a much better indicator of the demand in that area and a much better predictor of where the prices are trending.

I take issue with lots of other points in Keith’s post like the no reputable organization who can document prices bit. Title companies routinely report the closing sale prices of the transactions they handle and I guess Keith forgot that all of the pricing data is right there in the public record.

I guess since statistics are too much for him actual facts might be too.