How the overall median close price can be up when individual area prices are down
Have you come across a situation where the overall median sold price is up, but the sold prices by geographic areas are down? Well, sometimes data looks weird, even when it's correct. This is one of those cases. The issue is rooted in the definition of 'median.' As a refresher:
Median: the midpoint in a given range of values; taken as the average of the two middle values when there are an even number of values
As you can see, unlike Average, Median is not a calculation at all. A simpler way to think about median is if you took all the close prices and ordered them from lowest to highest, the price in the exact middle of the list is the median price for those listings. It's not math, it's just the luck of the draw.
So back to our problem. I'll use a real world example we recently came across. There was an area where the combined Median Sale Price for the month was $575,000, a 1.8% increase from the prior month. However, in one of the individual areas the price was $600,000, a 1.6% decrease from the prior month. In the other area, the price was $520,000, a 1.8% decrease month-over-month. How is it possible that both cities showed a decrease in the price, but the cities combined showed an increase?
Let's start with the first area. There were a total of 253 closed listings that month. That means that the median price, after I ordered the listings from lowest to highest, was the one on the 127th row. That's where we got the $600,000 for the month. The other area only close 89 listings, make the one on row 45 the one in the middle at, you guessed it, $520,000. In order to get the combined median for both areas, we had to put both lists together and sorted once more from smallest to largest. This time there were 342 listings, making the average between the listings on rows 171-172 the actual median. In this case, both of those listings sold for $575,000, so that was the median price; it was up from the prior month.
Area 1 ordered list Area 2 ordered list Combined ordered list
If you look again at those areas, the one with more closed sales was the one with higher prices. So when we combined both areas, there were more higher priced listings contributing to the list. So the combined result naturally trends higher. As a last note, this case was also unique because the increases and decreases we're discussing were in the low single digits. If just a handful of homes sold for less that month, the median would've shifted the down to closer to $550,000, which would've then been a decrease in the combined total. And we never would've received this question.
Some Final Thoughts...
If you're still reading, you may be thinking to yourself "this is why I like average price better." Don't get caught in that frame of mind because statistically, average is wrong for home prices. You can read the full explanation, then consider our example again. I'm just saying, if I'm trying to buy a home in area 1, the median price is a lot more palatable than the almost 30% higher average price!
AREA 1 | AREA 2 | COMBINED | |
MEDIAN PRICE | $600,000 | $520,000 | $575,000 |
AVERAGE PRICE | $777,017 | $556,283 | $719,575 |
DIFFERENCE | 29.5% higher! | 6.97% higher! | 25.14% higher! |
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