Average vs Median Sale Price
Ever wonder why the media and real estate boards quote average prices rather than the median sale price of homes? The reason is because headlines with higher numbers grab far more attention.
Average and median home prices are usually very different. Sale prices aren't evenly distributed because there are large gaps in price between the least and most expensive homes. This price gap skews the average price even moreso in larger statistical groups such as the average home price of an entire city.
Fully two-thirds of all Calgary houses sold in November sold for less than the city's average sale price of $516,447. Only 1% of all Northeast Calgary homes sold for more than the average sale price for the entire city.
By looking at recent Calgary home sales data we'll see why the average and median sale prices are so different. First, a quick review of the difference between Average Sale Price and Median Sale Price.
What is the Average (Mean) price?
The average price, also referred to as the mean price, is the grand total of a set of numbers divided by how many numbers there are:
i.e.: (3+6+8+23+35)/5 = 15
What is the Median price?
The median price is the middle value of a series of numbers, regardless of how low or high the numbers are above or below it. It’s easy to calculate: sort all the numbers in either acending or decending order, and the number in the middle of the group is the median value:
i.e.: (3+6+8+23+35) the 3rd number (8) is the median value
ProTip: The median value of even-numbered sets of numbers is the average of the middle pair of numbers.
Why Average & Median Sale Prices are so different
The extreme range of Calgary home sale prices skews the average sale price, evidenced by the number of sales vs. price range below:
"The average price increase is misleading as multi-million dollar sales skew the figures up" ..... Ann-Marie Lurie, CREB Economist
Large apparent peaks in the sales curves are the price points with the highest frequency of sales [known statistically as the central tendancy or mode]. In a normal range of numbers, these peaks are very close to both the average and median prices. All of the curves, with the exception of NE Calgary, have a distinct second peak at higher price ranges, typical of what's referred to as a bimodal distribution.
The tendancy of sales curves to lean or skew to the right of the central point to is characteristic of positve skewness. Each of the sales curves above display positve skewness - a reflection of more sales at the higher price ranges than the lower.
With the exception of NE Calgary, all of the sale curves show home sale prices well above $1,000,000
- NE Calgary Skewness = 0.7
- NW Calgary Skewness = 2.1
- SE Calgary Skewness = 2.5
- SW Calgary Skewness = 2.8
- Combined Calgary Skewness = 3.6
The more skewed or greater the Skewness is from 1.0, the more substantial the distribution of sale prices is. Symmetrical data has a skewness of 0, while asymmetrical (skattered) data has a skewness of greater (or less than) 1.0.
Skewness is calculated using the EXCEL function =SKEW( )
Notice the difference in the average and median sale prices within the 4 quadrants of Calgary? The average sale price of a Northeast Calgary home is one-half of what a Southwest home sold for. At the same time, the standard deviation (σ) of a Southwest Calgary home is 58% of what the SW average price is.
What is Standard Deviation?
Many of you may have forgotten the concept of standard deviation. This explanation provides non-mathematicians with a better understanding of how a group of numbers with sale prices outside of a normal range can influence the average sale price.
Standard deviation is the measure of the how much, on average, each number in a group varies from the average of the entire group. The lowercase greek character sigma is the symbol for standard deviation: σ
If all sale prices are within 68% of the group average, the standard deviation would be low (within +/-1 standard deviation). 2 sigma's (standard deviations) represent 95% of all numbers, while 3 sigma's, aka the "three-sigma-rule", represent 99.7% of all numbers in a normal distribution.
Standard deviation can be calculated using the EXCEL function =STDEV.P( )
Consider Median Sale Price rather than Average
When looking at Calgary real estate sale price changes we'd suggest disregarding the average price and focus on the median sale price, especially when looking at price change trends. Calgary real estate prices are widely scattered in all four quadrants of the city, meaning average sale price is skewed far more by many expensive home sales than by the occasional low-priced foreclosure or short sale home.
If you have any comments or questions, please feel free to comment. All Calgary Sales data used in this analysis is available via EXCEL spreadsheet.
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