Average Price Vs. Median Price

My mother is a math professor, so I speak in numbers.  There is an important difference between the median and the average, even though the two terms are often used interchangeably.  In today’s statistics lesson, I will define the two terms and illustrate the difference with some San Francisco real estate market statistics.  It will be a quick and painless math lesson, I promise.  Bear with me.  :-)

median – To find the median value, all the numbers in the sample are placed in order of value and the number in the middle is the median.  The easiest way to remember “median” is to simply call it “the middle number”.  The number 3 is the median number in the following sample:

1
1.5
2
2.5
3
3.5
4
4.5
19

When the sample is listed in ascending value, you’ll see the number 3 has four numbers before it and four numbers after it.  It’s the one in the middle, aka the median.

average - The average is the number that most accurately represents a data set (also known as the “mean”).  To find the average value of a set of numbers, the numbers are first added together, then divided by the total number of inputs.  Take the same sample used above:

1
1.5
2
2.5
3
3.5
4
4.5
19

Added together, the sum is 41.  The next step is to divide the sum (41) by the number of inputs in the data set (there are 9 of them in our example).  41 divided by 9 equals 4.56.
So, the median is 3 and the average is 4.56.
Why should you care?
The median is usually the most accurate representation of a set of numbers, like with home prices.  Averages are misleading because they include the outliers–the very large and the very small numbers that skew the results.  The average price per square foot in San Francisco is a much different number than the median price per square foot in San Francisco.  While they both follow the same trajectory over time, the difference appears because some high-priced properties skew the average.  The chart below shows the past few years of median price per square foot and average price per square foot in San Francisco. (red line is median price, yellow-greenish line is average price)
The trend illustrated for the entire city of San Francisco is interesting to understand the macro trends, but it’s not really useful.  Overall San Francisco real estate market trends are not nearly as relevant as zip code trends and neighborhood trends.  Also, some interesting changes become apparent when the timeline is shortened to the past six months.
The median price per foot is more stable and more accurately reflects the spring market in San Francisco.  The average price per foot is creeping higher as the high-priced listings enter the market.  In San Francisco, the numbers regularly skew higher rather than lower.  In many markets, the distressed housing inventory brings the average price down.  In San Francisco, sellers are fortunate enough (and buyers are unfortunate enough) to have a different issue.
The moral of story is to pay close attention to the real estate market statistics that tell you the most.  At the end of the day, there are a variety of factors that determine market value and every property is unique.  The only way to know for sure what a property is worth is to put it on the market and see what a ready, willing and able buyer is willing to pay for it.