Lies, Damn Lies, and Statistics:
Episode 1: Why Realtors Misread Data (and Why It Matters)
Lies, Damn Lies, and Statistics:
Why Realtors Misread Data (and Why It Matters)
Introduction
There is an old line, often attributed to Mark Twain, that there are three kinds of lies: lies, damned lies, and statistics. Real estate agents are particularly fond of the last category. Numbers are easy to cite, harder to interpret, and almost impossible to resist when they tell the story one wishes to tell. But data without context is worse than no data at all. To see why, we need only return to the basics of Statistics 101.
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The Median Card Trick
Take a standard deck of cards. Assign Ace the value of 1, count up through King as 13. What is the median card?
The answer is straightforward: it is the 7. Half of the values fall below it, half above. The mean (average) is also 7. In a perfectly ordered set, mean and median converge.
But even this simple deck demonstrates the fragility of those measures. Add extra Kings, remove the 2s, or slip in a Joker, and the mean shifts, the median moves, and the “center” of the deck is suddenly different. The deck has not changed size, but the way we measure it has changed the story we tell about it.
This is the first caution: statistics are not absolute truths; they are reflections of how we choose to slice a dataset.
When the Deck Shrinks
Now suppose we do not observe the entire deck of 52 cards. Instead, we draw only three cards at random. What happens to the median then?
Draw a 3, a 7, and a King: the median is 7.
Draw a 5, a 6, and an 8: the median is 6.5.
Draw a Jack, Queen, and King: the median is 12.
The “middle” jumps unpredictably.
And here is the crucial point: the average also jumps. With small samples, both measures bounce around because the law of large numbers has not had a chance to settle the volatility. The story changes not because the world changed, but because the sample was too small to provide stability.
This is the law of small numbers: randomness masquerading as signal.
Average vs. Median in Small Samples
Consider one more draw: a 3, a 7, and a King (13).
The median is 7.
The average is (3 + 7 + 13) ÷ 3 = 7.67.
Close enough. But change the sample: draw a 2, a 3, and a King.
The median is 3.
The average is 6.
Here the difference is dramatic. The median remains tied to an actual observed value, while the average is distorted upward by the outlier.
In small samples, averages are especially vulnerable to distortion. One extreme value can pull the mean into territory where no real observation lives. Medians, though imperfect, tend to be more representative of the “typical” case.
The Year-Over-Year Trap
This brings us to real estate. Realtors love to announce:
“Prices are up 10% compared to last year.”
“Inventory is 15% lower than this time in 2024.”
Such statements sound authoritative. They are also often meaningless.
The problem is twofold: first, the sample size; second, the choice of comparison point. A single month or even a single year is too small a sample to reveal a genuine trend. Point-to-point comparisons can exaggerate noise and disguise the signal.
Consider apples. If one has a single apple and acquires another, the supply has doubled — an increase of 100 percent. But if one has 100 apples and adds one more, the increase is 1 percent. The same action, two entirely different stories.
This is the law of low numbers.
In housing markets, it often plays out like this: last year’s median sale price in a neighborhood was $1.5 million; this year it is $1.65 million. An agent proclaims, “Prices are up 10 percent!” But step back: three years ago, the peak was $1.9 million. Today’s $1.65 million figure is still 14 percent below that high. The “increase” is not evidence of a boom; it is evidence of a partial recovery.
Why Trends Matter More Than Points
Point-to-point comparisons tell us little. Trends tell us much more. A series of medians plotted over time shows the trajectory of a market. Are prices climbing back toward previous highs? Are they plateauing? Or are they declining further despite temporary upticks?
The key is to treat individual data points with suspicion. Just as a three-card draw cannot reveal the nature of a 52-card deck, a one-year comparison cannot capture the underlying dynamics of a housing market. Only by examining larger samples across longer time horizons can one approach the truth.
Conclusion
The moral is clear. Numbers do not speak for themselves. They require interpretation, context, and scale. Medians are often more reliable than averages, but both can mislead when drawn from too few observations. Point-to-point comparisons flatter to deceive; trends reveal reality.
In real estate, as in economics, the law of small numbers is unforgiving. Without understanding its traps, agents risk presenting randomness as fact and noise as narrative. And that, as Twain might have said, is the most dangerous lie of all.