Guide: Price Distributions and Indices

TL;DR

Our Distribution Model generates the full price distribution of a property market. It reveals how prices cluster, how wide the spread is, and whether there are distinct submarkets. It's also the foundation for summary statistics such as the median and geometric mean. Having the full distribution means you can extract any of these measures and track them over time.

From Histograms to Continuous Distributions

The easiest way to develop some intuition about how distributions work is to look at how they relate to histograms. A histogram of property prices shows the number of properties that fall into each bin^*A bin is a bucket that groups values within a range. For example, a bin from $500K–$600K contains all properties priced in that range. . Start with a histogram with eleven bins between $0 and $4M:

The histogram is coarse, but it shows that most properties range from $0.5M to $2M. The peak is somewhere just below $1M. Increasing the number of bins makes things clearer. At each step, more detail appears about where precisely the property values cluster and, with enough bins, the histogram starts to resemble the smooth curve of the underlying probability distribution.

A histogram is used to show how many sales occurred in a specific price range. In contrast, the distribution tells us the relative odds of finding a property at any given price point. Note that the units of the Y-axis here are "density". Higher density at a particular price means there is a higher concentration of properties around that price.

While the animation illustrates the concept, there's an important distinction worth mentioning. The histogram is counting real property transactions that occurred. It's inherently incomplete and biased since not all properties sell, and those that do may not represent the full market. It may be that many three-bedroom houses sold in one month, but it was mostly four bedroom-houses that sold the next month. A histogram of property sales would make it appear that prices went up, even though only the mix of sales changed. The distribution is modelled. It uses information from the sales to estimate the distribution of property values across the whole market, not just those that sold.

Understanding Distribution Shapes

The shape of a price distribution varies from market to market, and reveals something about its structure that a single summary statistic (like the median) can't convey on its own.

A 'normal', or 'bell curve' distribution shows a market where prices group evenly around a central value. Most property markets, especially mature ones, aren't normally distributed. They tend to be 'log-normal'. The log-normal distribution has a single peak like the normal distribution, but skews right with a 'long tail' of expensive properties stretching out towards high prices. Due to the nature of property price growth, prices will tend to evolve towards a log-normal distribution over time. See our post on central tendencies for more detail.

In some markets, especially those in large and diverse cities, you'll see multimodal distributions. Here, there are multiple peaks that correspond to distinct sub-markets. This might reflect an established high end market coexisting with new developments at lower price points. When each segment contains enough properties, they show up as distinct peaks.

Two distributions can look quite different while sharing similar summary statistics. Consider Melbourne and Port Macquarie: both regions have a median house price around $950k. Port Macquarie is fairly log-normal with a prominent single peak. Melbourne's distribution extends broadly out towards higher prices with a small secondary peak around $1.4M. Melbourne features a wider range of prices and a higher proportion of high-value properties. The experience of buying or selling a property in these two markets will be very different, despite their median prices being the same.

Extracting Summary Statistics

Different questions need different measures, and having the full distribution means you can use the one that fits best. While the median is often a good choice, there are times when the mode, geometric mean, arithmetic mean^*Often referred to as the average, or shortened to 'mean'. , or some other measure will be more appropriate.

Some statistical measures are quite directly related to the distribution shape. The mode (the most common price) corresponds to the peak of the distribution curve, while the median divides the area under the curve in half. The mean isn't tied to a specific point on the curve, but is influenced by the entire shape of the distribution. The Adelaide house price distribution shows how these measures spread out across a real market.

The mode, median, geometric mean, and arithmetic mean each land in a different spot along the curve. Depending on the distribution, they might be close together or spread far apart. Central tendencies aren't the only thing that can be extracted. The width of the distribution is itself a valuable summary statistic, and one that can only be properly measured when you have the whole distribution to work with.

Evolving Distributions

Price distributions aren't static. They change over time as the market evolves and the summary statistics shift along with them. This animation pairs the distribution (with its median marked) alongside the time series that emerges from tracking that median as the market evolves.

This is exactly how our Distribution Index works. The underlying model generates the full distribution for each property type in each region at each time. We then pull out summary statistics for each one to produce a whole variety of indices. The distribution gives the full picture so we see exactly how Australia's property markets are changing over time.