The Geometric Mean for Property Price Indices

A property price index needs to summarise an entire market with one number. That sounds straightforward, but it raises a big question: which number?

This is about finding the central tendency - a single value that best represents the centre of the data. But which measure you choose matters enormously. Our monthly updates use the geometric mean because property markets grow multiplicatively, while our Distribution Index gives you the flexibility to switch to medians for typical costs or averages for total valuations.

Beyond Sale Prices

Before we look at central tendencies, we need to first clarify what we're measuring. A property price index differs fundamentally from reports of recent sale prices. Sale price history shows recent transactions. An index tracks the underlying market value.

This distinction matters because sales data can be misleading. For example, every December in Sydney, the median sale price drops.

But does every house in Sydney suddenly lose value at Christmas every year? Of course not. Sales volumes are low, and the properties being sold are mostly cheaper. The underlying value isn't changing; we're seeing a biased sample.

A good index filters out distractions. It focuses on real market movements instead of quirks from individual property sales.

With that base, let's look at three approaches to finding that single representative number for central tendency.

The Average: Capturing Total Market Value

The average, specifically the arithmetic mean, is the statistical measure that most people recognise. Its strength is in calculating the total market value. Multiplying the average by the number of properties gives the total worth of a portfolio or region.

This helps investors and financial institutions check portfolio size. Government agencies can also use it to calculate total property wealth in their area without needing individual valuations.

But the average is less appropriate when the sample of properties has a skewed price distribution. Take nine $400k properties and one $1M property. The average of $460k sits 15% above what's typical, pulled up by that single expensive home. On a larger scale, this illustrates how the average, as a measure of central tendency, tends to be pulled toward the tail of a skewed distribution. Still, multiply that $460k average by ten properties and you correctly get $4.6M - the true total value.

The average works best when you care about the combined value rather than finding what's representative.

The Median: Understanding the Typical Property

The median is the middle value: half the properties cost more; half cost less. It answers a fundamental question: what does a 'typical' property cost?

When you're house hunting in a new suburb, the median helps you compare prices. Is this listing above or below the typical price for the area? Unlike the average, the median is less sensitive to outliers. That $10M waterfront mansion won't skew your understanding of the local market.

Another example where the median is helpful is in discussing housing affordability and the cost of living. Since 50% of the homes are under the median house price, it can be compared to incomes to determine what is, or isn't, generally affordable.

But the median tells you nothing about variety. Two suburbs with $800k medians can vary greatly. One might be tightly clustered, with most homes between $750k and $850k. The other could include a mix of $400k and $1.2M houses. Same middle value, very different markets.

The median excels at finding the centre. When you need to understand the typical property for buying, selling, or comparison, it's a useful guide.

The Geometric Mean: A Tool for Multiplicative Markets

Property markets inherently rise and fall by percentages rather than fixed dollar amounts - what economists call multiplicative growth. This simple fact shapes how we measure these markets.

When a new train station opens, the value of every property in the suburb doesn't increase by the same $50k. The premium houses might gain $200k while modest units gain $30k. The gain is proportional to each property's existing value.

How Multiplication Creates Skewed Markets

The percentage-based growth of property markets naturally creates a skewed distribution of prices. The gap between expensive and cheap properties widens as each grows by consistent percentages over time. A 10% rise on $2M adds $200k, while the same 10% on $500k adds just $50k. In reality, the percentage changes aren’t exactly the same. There’s some variation from house to house, street to street, and so on.

Over the years and decades, as growth compounds, this multiplicative process stretches the market. You end up with many properties clustered at lower prices and progressively fewer as prices climb.

One Weird Trick

The stretched distribution we're discussing is known in mathematics as a log-normal distribution. It appears all the time in nature and economics. The size of icebergs, the incomes of your colleagues, and property prices all tend to be log-normal. Although not perfectly, and not all the time.

The trick is that when you take property prices and/or iceberg size and calculate the logarithm, the distributions appear symmetrical and well-behaved.

Another way to say this is that if you track property prices in dollars, you see a skewed distribution, and that causes problems for some central tendencies, like the average. But if you track them in terms of percentage changes or growth multiples, you're working in a way that’s better aligned with the natural way these markets change.

This is exactly what the geometric mean does. Rather than adding values like the arithmetic average, it multiplies them together and takes the nth root. This isn't arbitrary; it's the mathematical equivalent of converting to logarithms, finding the average, and converting back.

As a result, it gives a solid representative number for tracking how property markets actually move over time.

Our Monthly Updates

The geometric mean is less familiar than the average or median. However, it's well aligned with the basic, multiplicative nature of property markets. It's also very handy for calculating compounding growth. That's why it's an industry standard, why we use it in our monthly updates, and why we reach for it in much of our day-to-day reporting on property price movements.

The geometric mean answers: what's the most representative value when markets move by percentages?

There are, however, still plenty of reasons you might reach for another tool.

The D Index

Since our Distribution Index captures the entire distribution of property values, we can calculate any statistical measure or central tendency we like.

This means you can select the right measure for each specific question. Comparing property affordability against ABS median household incomes? The median property price provides the most meaningful comparison. Researching what to expect when house hunting in a new suburb? The median shines here too. Need to estimate the total market value of a council area or large portfolio without individual valuations? Multiply the average by the property count.

The flexibility extends beyond the familiar measures. Because the D Index maintains the full distribution, it can answer more nuanced questions. What's happening at the premium end of the market? The 95th percentile tracks those high-value properties as a distinct category from the broader market. How compressed or spread out are property values in different regions? The distribution reveals market diversity that no single number can capture.

Every market question gets the statistical measure it deserves.