Median: What Does it Mean?
In a world of statistical averages, many have asked why the Economic Research Group of the NATIONAL ASSOCIATION OF REALTORS® reports a median home sale value instead of a mean in its monthly Existing-Home Sales reports (as well as most of its other industry statistics). There are many people who believe the mean is easier to understand than the median. But the median measure is not difficult to appreciate. Let's start with defining and differentiating between the two measures.
A mean is calculated by adding up all the values in a distribution and then dividing the sum by the total number of values contained in that distribution. To find a median value, one takes all of the values in the distribution, sorts in ascending order, lines them up and finds the middle value.
They sound similar, and in may instances, there is not much difference between the two values. But the reason NAR concentrates on the median instead of the mean is because the mean value calculation has a limitation that can prevent it from reflecting an "average." In calculating home sales price statistics this limitation occurs when the sale price of one home varies greatly from the remainder of the homes. This can skew the average.
For instance, suppose we encounter a small town calculating its home sales statistics for March of 2000. In March, six homes in Smalltown, USA were sold at the following prices:
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In this situation, the mean would be $105,000, the median would be $105,000, and everything works out great.
But suppose instead of six homes, seven were sold and the seventh home sold for $250,000. Now the median would be $110,000, but the mean would dramatically increase to $125,700. Yet, only two homes sold for more than the mean, while five sold for less.
This type of situation can be seen in the U.S. home sale price distribution for March 2000. The median price, however, indicates half of the homes sold for more and half sold for less. The mean has been pulled from the apex of the distribution by the 5% of the homes that sold for more than $500,000.
It is important to notice the distribution of home sales is not a normal bell-shaped distribution. Rather, there are a high number of sales in the lower end of the price scale, which produces a long tail sloping down toward the lower end of the scale. This type of distribution shows it would not be appropriate to emphasize the mean price of $175,300 when the majority of the homes sold in the $100,000-$160,000 range. The median price of $136,900 better reflects the selling price of homes in a given time period.
While the mean price may be useful in discussions on aggregate home sales and dollar volume of home sales, the "average" homebuyer/seller learns more about the price of a typical home from the median price. If buyers and sellers respond to the mean price of $175,300, "average" sellers may have set the asking price too high. Buyers could be misled into believing they cannot afford to purchase a home. This would discourage people from entering the market and be counterproductive for the real estate industry.
