## Tuesday, May 19, 2009

### Median Price Mix Example

by Bill McBride on 5/19/2009 05:35:00 PM

The following table shows how the mix of units can skew the median price. This is just an example (not based on actual data).

In this example, from 2002 to 2005 low priced homes doubled in price, and high priced homes increased by two-thirds. The mix remained the same (50 units of each), and the median price increased 75%.

Median Price Example
Item20022005200720092010
Low Price\$100\$200\$200\$100\$100
High Price\$300\$500\$500\$400\$300
Low End Units Sold5050404020
High End Units Sold5050501030
Median Price\$200\$350\$500\$100\$300
Change in Low Price--100%none-50%none
Change in High Price--67%none-20%-25%
Change in Median Price--75%43%-80%200%

Now look at what happened in 2007. Since subprime imploded first, the number of units sold at the low end decreased to 40 from 50. Everything else stayed the same - and just the change in the mix (higher percentage of high end homes) pushed up the median price! Note that the median price (light blue) increased WITHOUT any actual prices increasing. This happened at the beginning of the housing bust in many areas.

In the period I marked as 2009, the low end prices have fallen all the way back to 2002 prices. However the high end prices have only fallen 20%. The low end is seeing fairly high activity (40 units), but at the high end sales activity has collapsed (10 units). Look at the median price (in orange) - it has fallen more than the prices have declined for even the low end!

And finally, in 2010, prices fall further at the high end - and have stabilized at the low end. As prices fall, the volume picks up at the high end. And what happens to the median price? It increases by 200% (marked in red)!

UPDATE: Oops - I used average instead of median a couple of places (sorry - technical problems today),

This illustrates why we need to be very careful with median prices (like from NAR, DataQuick or other sources). The mix can distort the price, and I expect to read about median prices increasing later this year or in 2010, even though actual prices are still falling!