The Mesmerizing Magic of the Median: Statistical Sleight of Hand?


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the proverbial kinds of falsehoods, lies, damned lies, and statistics (Mrs. Andrew Crosse, 1892)

Every Housing Report, whether by NAR, appraisal firms or AVMs, touts the magic word “median” to imply that the results are a true reflection of market reality. Read the articles in any newspaper or online source and this magic word is sure to appear. For those who have not studied the magical and sublime craft of statistics, Median, Average’s fraternal twin, is simply the middle number in a range of numbers. There are as many results above the median as below it. An average, on the other hand, is the sum of the data divided by total number of results.

An example: 100,000 200,000 300,000 301,000 1,000,000 2,000,000 5,000,000. The median is 301,000 while the average is approximately 1,270,000. The numbers can represent actual sales, AVM unsold values or AVM error rates. Can you tell me which better reflects reality? Perhaps neither. The raw data is the reality, the statistical computation an attempt to pull meaning from it. Does it?

James Surowiecki (author of the Wisdom of Crowds), in his recent article in The New Yorker entitled “Safe as Houses”, argues that the median may not be a useful statistic when deciding whether to invest in real estate.

Unfortunately, the numbers upon which these comforting conclusions depend—namely, median home prices for the country—are unreliable and misleading…. if you’re trying to figure out what kind of investment housing is—what rewards you can expect and what risks you’ll run—median prices become a lot less useful. In the first place, the data don’t adjust for improvements in quality….And the impact of quality adjustments isn’t trivial; a study of home prices between 1977 and 2003 found that adjusting for quality reduced the return to homeowners by forty per cent….What makes the problem worse is that sellers have recently been offering buyers huge incentives, ranging from granite counters to free cars and, in some cases, large rebates. These are, in fact, price cuts, but they never make it into the data.

Then, there’s the problem of sample bias….(which can) lead to the curious phenomenon of median prices rising even as the number of sales is plummeting and the backlog of houses on the market is soaring. Because nominal median prices compare completely different groups of homes (all those sold in August, 2005, say, and all those sold in August, 2006), they can overstate how much prices go up during booms and understate how much they go down during busts.

For those who want to know how the magician statistician performs his trick, read the article, otherwise remain entertained by the show.

9 Responses to “The Mesmerizing Magic of the Median: Statistical Sleight of Hand?”


  1. 1 Doug Quance Nov 13th, 2006 at 1:02 pm

    I’ve been meaning to write an article like this… so I am glad you brought it up.

    Both median prices and average prices are indicative of a market, but without careful analysis - they can paint a story that doesn’t exist.

    Let’s say, for example, that Daddy Warbucks comes to a town with a median price of $300,000 and tells all the poor people that are currently renting “Come to me, and I will loan you enough money to buy a $100,000 house. Everybody qualifies!”

    And so they do.

    So all the activity in that sector of the housing market would force a decline in the median price… as well as a decline in the average price. Not to mention a dip in rental occupancy rates.

    Did this activity have a negative effect on the upper sectors? Not necessarily. But it could leave the uninformed to believe so.

    The one thing that these statistics do show is trends… and while trends are useful, they do not tell the whole story.

  2. 2 Athol Kay Nov 13th, 2006 at 1:38 pm

    Over a large sample the more meaningful the median becomes. In a five unit sample it’s pointless, but in a 100+ sample it’s more interesting. Generally you have to look at both the median and the average to get useful information.

    In the end there are only a few ways to look at local housing data, this is one of them.

    I do agree that the increase in housing quality is a lost factor though. Once upon a time a 1000sqft house was normal, and now it’s a bargain basement property.

  3. 3 sellsius° Nov 13th, 2006 at 2:07 pm

    Surowiecki’s article was interesting to me because it showed that statistics like median, taken alone, may not tell the whole story and that housing has unique unzills that do not even get in the data.
    I was fortunate to have studied statistics under a professor who was notorious for exposing the secret tricks of stat spinning to create a certain picture.

  4. 4 Sam Chapman Nov 13th, 2006 at 4:07 pm

    The median price of a home in Austin is also deceiving. For the month of September, 2006, the median price of a home in the Austin area was $167,000. This sounds great and is much of the reason investors are flocking here. When you look at the Austin market (as in many markets), more home sales are happening in lower priced areas than in higher priced areas. The lower priced areas tend to be to the somewhat distant south, east and north of the downtown area. This is where you can find homes for the median price or even the average price, which was just under $228,000 in September.

    Now what are the most appealing areas of Austin? Close to downtown and the University of Texas is very popular. To the west in the limestone Hill Country and on or near Lake Travis is also incredubly popular. The problem is that many people think of hills and lakes when thinking of Austin. They see the “cheap” price of homes and think they can get into a nice Hill Country home with a lake view for $250,000. Sorry, but this isn’t reality.

    If you’re close to downtown or UT, you can get into a 1200 square foot home for under $300,000 if it needs a bit of work. On Lake Travis, you might get into a tear-down on the south side of the lake with fair lake frontage for around $600,000 if you’re really lucky. A nice Hill Country home on an acre might go for $550,000 or so, more if it has a lake view.

    So don’t be fooled. Sure Austin is an incredible place to own a home, but be prepared to really get educated before expecting anything.

  5. 5 sellsius° Nov 13th, 2006 at 4:13 pm

    Excellent insights on your market Sam. Thank you for sharing real life experience, a much better teacher than statistics.

  6. 6 Andrew Hodge Nov 16th, 2006 at 5:05 pm

    I have posted on this in the past as well. It is not just the median prices that one has to worry about but also the “average sale price”, “average days on market” and “sale to listing price ratios”. The reality is that none of these statistical values truly relates to any particular type of home. The value of a 2500 square foot home can decrease and you can still have an increasing average sale price if buyers decide to push for bigger homes instead of taking the savings, on the home they would have bought if prices did not drop, or they could be changing the type of housing that they want, say from a condo to a detached freehold home or back.

    In Richmond Hill the “Average sale price” for October 2006 was up about 8% from 2005 but this does not reflect the true market that has only seen a raise of about 2-3% for a given home. All of these numbers have a greater relationship to buyer activity than to home values.

    As for “Days on market” and “sale / list price ratios” these are probably the most manipulable values, and many agents re-list or price change homes, just prior to registering the sale so that they can market the home as sold in 5-10 days for 100% of the asking price.

    The bottom line is that the only way to see real trends or value is by looking at the recent activity of comparable homes on a regular basis. Which is why not every agent is as good at knowing the market as others.

  1. 1 NAR Reports Sales Down Nationally at sellsius° real estate blog Pingback on Nov 27th, 2006 at 3:51 pm
  2. 2 Trulia Trend Report Released at sellsius° real estate blog Pingback on Feb 15th, 2007 at 2:04 pm
  3. 3 How to Lie About California Foreclosures: Use Statistics Pingback on Oct 20th, 2007 at 11:54 am

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