The Mean Is a Bet, the Median Is a Description: Skew, Central Tendency, and the Two Numbers That Decide Real Estate Deals
Two brokers walk out of the same submarket tour on the same afternoon.
The first one says the market is at $2,340 a month. The second says the market is at $1,950. Neither is lying, neither made an error, and both pulled from the same rent roll. The first quoted the mean. The second quoted the median. The $390 between them is not a discrepancy to be reconciled. It is a measurement, and it is telling you something specific about that submarket that neither number tells you on its own.
Most people in this business know that mean and median are different. Far fewer can say precisely which one belongs in which cell of a model, and that gap is expensive. It shows up as market studies that justify rents nobody in the trade area can pay, contingencies that are systematically undersized across a program while feeling generous on each individual job, appraisals that swing by millions on the choice of a summary statistic, and track records that report returns the sponsor did not actually earn.
This is the full treatment. What the two statistics actually are, what the distance between them measures, and then a worked case for each of the decisions where getting it wrong costs real money.
Part I: They Are Answers to Two Different Questions
The textbook definitions are correct and useless. The mean is the sum divided by the count. The median is the middle value. Everyone knows this and it explains nothing about when to use which.
The useful definitions are these:
The mean is the balance point. Lay the distribution on a plank and the mean is where you would put the fulcrum. It is the center of mass. Every observation pulls on it, and it pulls in proportion to how far out the observation sits.
The median is the middle of the count. It is the value where half the observations are above and half below. It is the center of population. Each observation gets one vote regardless of size.
That is the whole distinction. The mean is a democracy of dollars. The median is a democracy of units.
There is a deeper version, and it is worth carrying because it resolves almost every practical question. Each statistic is the solution to a different optimization problem.
The mean is the value c that minimizes the sum of squared deviations, Σ(x − c)². The median is the value that minimizes the sum of absolute deviations, Σ|x − c|.
Squared error punishes being far off much more than being slightly off. Absolute error treats a $1,000 miss as exactly twice as bad as a $500 miss. So the choice between mean and median is really a statement about your loss function. If a large error hurts you disproportionately, and it usually does when the error is in a total you have to fund, use the mean. If an error costs you in proportion to its size, and it usually does when you are pricing one unit at a time, use the median.
And then the identity that settles more arguments than anything else in this article:
Total = mean × count.
The mean is the only measure of central tendency that reconstructs the aggregate. Median times count is a meaningless number. It corresponds to nothing.
From that single fact, the rule falls out:
If you are going to multiply it by a count, you need the mean. If you are going to experience it once, you need the median.
Total rent roll, total development cost, total absorption, total loss reserve, total NOI: all sums, all mean. What the next tenant will pay, what the next unit will sell for, how long the next lease-up will take, what a typical household in the trade area earns: all single draws, all median.
Almost every error in the rest of this article is a violation of that one line.
Part II: What the Gap Measures
When mean and median are equal, the distribution is symmetric. When they diverge, the distribution is skewed, and the direction of the divergence tells you which tail is doing the pulling.
Mean above median means right skew. A long tail of high values. This describes nearly everything in real estate: rents, sale prices, household incomes, construction cost overruns, lease-up durations, land values, deal sizes. The reason is structural. All of these variables are bounded below by zero or by some floor, and unbounded above. Rent cannot go below zero. It can go to $18,000 for a penthouse.
Mean below median means left skew. Rare in this business, and when you see it you should look hard, because it usually means a ceiling is binding. Occupancy is the classic case: a stabilized portfolio's occupancy is bounded at 100 percent and has a tail of troubled assets below, so the mean sits under the median. Rent-controlled or income-restricted rent rolls behave the same way, with the cap creating a pile-up at the top.
There is a fast field diagnostic. Pearson's second coefficient of skewness:
Skew = 3 × (mean − median) / standard deviation
Rough interpretation: under 0.5 in absolute value is roughly symmetric, 0.5 to 1.0 is moderately skewed, above 1.0 is strongly skewed and the mean should not be quoted without an explanation attached.
There is also a more elegant version available when the variable is approximately log-normal, which most real estate price and rent variables are. For a log-normal distribution:
- median = e^μ
- mean = e^(μ + σ²/2)
Therefore mean / median = e^(σ²/2) exactly.
The ratio between the mean and the median is the dispersion. Nothing else. This gives you a way to read a distribution's spread from two numbers on a broker's page.
| Log-scale dispersion σ | Implied mean/median ratio | What that looks like |
|---|---|---|
| 0.15 | 1.011 | A homogeneous product type, one vintage |
| 0.25 | 1.032 | A normal single-asset rent roll |
| 0.35 | 1.063 | A mixed-vintage submarket |
| 0.45 | 1.107 | A submarket in transition |
| 0.55 | 1.163 | Two markets sharing a zip code |
| 0.70 | 1.280 | Not a market, a collection |
Run that backward on the two brokers from the opening. Their ratio is 2,340 / 1,950 = 1.200. Solving, σ² / 2 = ln(1.200) = 0.1823, so σ² = 0.365 and σ = 0.604.
That is enormous dispersion for a single submarket. Before you look at a single comp, the arithmetic has told you that this is not one rental market. It is at least two, probably a pre-1990 workforce stock and a recent-delivery Class A stock sharing a geography and nothing else. Any single "market rent" number for that submarket, mean or median, is a fiction. You need to segment before you underwrite, and you knew that from two numbers and a logarithm.
That is the highest-value use of the mean-median gap: not choosing between them, but reading the distance as a signal that tells you when to stop summarizing and start segmenting.
Part III: The Rent Roll
A 200-unit property. This is the actual distribution.
| Unit type | Count | Average rent | Total monthly rent |
|---|---|---|---|
| Studio | 40 | $1,450 | $58,000 |
| One bedroom | 88 | $1,780 | $156,640 |
| Two bedroom | 48 | $2,320 | $111,360 |
| Three bedroom | 12 | $3,050 | $36,600 |
| Penthouse | 12 | $6,400 | $76,800 |
| Total | 200 | $439,400 |
Mean rent = $439,400 / 200 = $2,197
Median rent: sort all 200 units. Units 1 through 40 are studios, 41 through 128 are one-bedrooms. The 100th and 101st units are both one-bedrooms, so the median is $1,780.
The gap is $417, or 23 percent of the median. Standard deviation across the rent roll is $1,138, giving a Pearson skew of 3 × 417 / 1,138 = 1.10. Strongly right-skewed, and the mean should carry a warning label.
Where the skew comes from and what it costs
Twelve penthouses. Six percent of the units, producing $76,800 of the $439,400 monthly rent, which is 17.5 percent of the revenue.
Delete them and rerun. The remaining 188 units produce $362,600, a mean of $1,929. The median does not move at all: still $1,780. Removing 6 percent of the units moved the mean by $268, or 12 percent. That is the fragility of the mean stated precisely: it is a weighted average where the weights are the values themselves, so a small number of large observations carry disproportionate influence.
Now the decisions.
Underwriting the renewal bump. Use the mean. You are projecting total revenue, which is a sum, so mean × count is exact. Apply a 4 percent bump to $2,197 and multiply by 200 and you get $457,000 of monthly potential rent, which is correct to the dollar. If you tried this with the median you would get $370,240, understating the rent roll by $86,760 a month and a bit over a million dollars a year.
Pricing the next vacancy. Use the median, or better, use the segment. If you tell the leasing team the property averages $2,197 and to price accordingly, you will price a one-bedroom 23 percent above what one-bedrooms in this building actually achieve. The unit will sit. And because a vacant unit costs you full rent while a mispriced-low unit costs you only the shortfall, the asymmetry compounds against you.
Assessing risk concentration. Use both, and look at the tail explicitly. The penthouses are 17.5 percent of revenue and they are the most cyclical stock in the building, because luxury rental demand is the most elastic and the most exposed to for-sale substitution. Model penthouse vacancy going from 5 percent to 30 percent in a downturn: 12 units × $6,400 × 25 percentage points = $19,200 a month, or $230,400 a year. That is 4.4 percent of gross potential revenue lost from 6 percent of the units. Capitalized at 5.25 percent, it is $4.39M of value, on an asset whose total value at that cap rate is around $80M.
Note what happens to your reporting during that downturn. The mean rent collapses toward $1,929 as the penthouses go dark and get discounted. The median does not move a dollar. An asset manager watching the mean sees a crisis. An asset manager watching the median sees nothing. You need both, and you need to know which one moved and why.
The general rule for a rent roll: the mean is your revenue engine, the median is your product, and the gap between them is your concentration risk. Report all three.
Part IV: Comparable Sales, Where the Mean Costs Millions
Nine multifamily trades in a submarket over eighteen months, on a price-per-unit basis:
$168k, $175k, $181k, $186k, $192k, $198k, $205k, $214k, $385k
Mean = $1,904k / 9 = $211.6k per unit
Median = the 5th value = $192k per unit
One comp, the $385k trade, is a brand-new structured-parking asset with a rooftop pool that traded to a core buyer. It is 11 percent of the observations and 20 percent of the aggregate dollars, and it pulls the mean 10 percent above the median.
Now value a 300-unit asset off that comp set:
| Method | Price per unit | Implied value | 65% LTV loan proceeds |
|---|---|---|---|
| Mean | $211.6k | $63.48M | $41.26M |
| Median | $192.0k | $57.60M | $37.44M |
| Difference | $19.6k | $5.88M | $3.82M |
A $5.88M valuation swing and $3.82M of loan proceeds, entirely determined by which of two equally legitimate summary statistics the analyst reached for. On a deal that size, $3.82M is the entire general partner co-investment. The choice of statistic is the deal.
The professional compromise
Neither raw number is the right answer, and the field has three better tools.
The trimmed mean. Drop the top and bottom observations before averaging. Trimming one from each end of the nine comps leaves $175k through $214k, which averages to $193.0k, within a percent of the median. The trimmed mean uses more information than the median while remaining robust to the outlier. For comp sets of eight or more, a 10 to 20 percent trim is a reasonable default and should be stated explicitly.
Winsorizing. Instead of dropping the extreme values, replace them with the nearest retained value. The $385k becomes $214k. This keeps the observation count intact, which matters when the sample is small, and it acknowledges that the trophy trade is real information about the top of the market even if its magnitude is unrepresentative.
Adjustment, which is the actual answer. The sales comparison approach exists because the right treatment of a dissimilar comp is not to delete it or shrink it, but to adjust it: for vintage, parking structure, unit size, submarket, and date of sale. Adjust the $385k trade down for its 2024 vintage against your 2009 vintage, its structured parking, and its 8 percent larger average unit, and it might land at $240k, at which point it belongs in the set. The mean of the adjusted set is a better estimator than the median of the unadjusted one.
The mean-median gap is the diagnostic that tells you adjustment is required. When they are within 3 or 4 percent, a quick screen off either is fine. When they are 10 percent apart, as here, the comp set is not homogeneous and no summary statistic will save you.
The same trap at the market level
Median home price is the most widely reported real estate statistic in the country and it is a poor price index, for a reason that has nothing to do with skew.
Median sale price measures the middle of what sold, not the change in value of what exists. If credit tightens and first-time buyers exit while move-up buyers keep transacting, the median sale price rises even if every single house in the market lost value. The composition of the transacting sample changed. This is exactly what happened in several markets in 2008 and 2009, where median prices printed misleadingly stable through the early part of the decline because the low end of the market simply stopped clearing.
This is why Case-Shiller and FHFA use repeat-sales methodology, comparing the same property to itself across two transactions. It is the only construction that holds the mix constant. Any time you see a median price series moving, your first question should be whether the price changed or the mix did, and the honest answer is almost always some of both.
The same mix contamination sits inside median rent, median cap rate, and median price per square foot in every market report you read.
Part V: Ratios Do Not Average
This is the most common purely mathematical error in real estate analysis and it is worth its own section, because it produces wrong answers in a direction people never check.
The mean of ratios is not the ratio of means
Two units:
- Unit A: 500 square feet at $2.60 per square foot = $1,300
- Unit B: 1,200 square feet at $2.00 per square foot = $2,400
Average the two rents per square foot: (2.60 + 2.00) / 2 = $2.30 per square foot.
Now compute the actual portfolio rate: $3,700 of rent over 1,700 square feet = $2.176 per square foot.
The naive average overstates by 5.7 percent. Scale that across a 300-unit rent roll with a mix skewed toward small units, apply it to a stabilized value calculation, and you have overstated the asset by several million dollars with arithmetic that looked unimpeachable.
The fix is that a ratio must be aggregated by summing the numerators and summing the denominators, or equivalently by taking a weighted mean where the weights are the denominators. Weight rent per square foot by square feet. Weight price per unit by units. Weight expense ratios by revenue. Never take a simple average of a column of ratios.
Cap rates are worse, because they are inverted
Cap rates are a ratio with value in the denominator, which means averaging them requires more care still.
You own two buildings, each generating $1.0M of NOI. One is valued at a 5.0 percent cap ($20.0M), the other at a 7.0 percent cap ($14.29M).
What is the portfolio cap rate? The naive answer is (5 + 7) / 2 = 6.0 percent.
The correct answer is total NOI over total value: $2.0M / $34.29M = 5.833 percent.
The naive arithmetic mean is off by 16.7 basis points, and at $2.0M of NOI that is the difference between a $34.29M portfolio and a $33.33M one. $956,000 of value created by an arithmetic error.
The right way to average cap rates depends on what is held constant. When NOI is equal across the assets, the correct average is the harmonic mean: 2 / (1/0.05 + 1/0.07) = 2 / 34.286 = 5.833 percent, which matches exactly. When NOI differs, value-weight the arithmetic mean, which reduces to the same thing.
The general principle: any time the quantity you care about sits in the denominator, the arithmetic mean is biased upward. That covers cap rates, yields, returns on cost, debt yields, and expense ratios expressed per dollar of revenue. In every one of those cases the naive average flatters you.
And you cannot average IRRs
The most consequential version of this error lives in track records.
A sponsor closes two deals in the same vintage:
- Deal 1: $1M of equity, three-year hold, 40 percent IRR
- Deal 2: $19M of equity, three-year hold, 8 percent IRR
The pitch deck reports the average deal IRR: (40 + 8) / 2 = 24 percent.
Compute what the investors actually got. Deal 1 returns $1M × 1.40³ = $2.744M. Deal 2 returns $19M × 1.08³ = $23.93M. Total in: $20M. Total back: $26.68M. Multiple of 1.334 over three years, which is a pooled IRR of 10.1 percent.
The reported average is 24 percent. The realized return is 10.1 percent. The sponsor did not lie about a single deal, and every individual IRR is correct.
Note that even equity-weighting the IRRs, which gives (1 × 40 + 19 × 8) / 20 = 9.6 percent, is not exactly right, because IRR is a nonlinear function of cash flows and does not aggregate linearly under any weighting scheme. The only correct calculation is to pool the actual cash flows and solve once.
When you read a track record, the questions are: is this a pooled IRR or an average of deal IRRs, is it gross or net of fees and promote, and what is the equity-weighted distribution of the underlying deals. A sponsor who has done one great small deal and nineteen mediocre large ones will show beautifully on an unweighted mean and should not.
Part VI: Contingency, Where the Median Feels Right and Bankrupts You
Cost overruns are the purest right-skewed distribution in development. Bounded below, because a job can only come in so far under budget before the estimate was simply wrong, and unbounded above, because a soil condition, a redesign, a subcontractor default, or a tariff has no ceiling.
One hundred completed projects, hard cost variance against the original GMP:
| Overrun | Projects | Cumulative |
|---|---|---|
| −2% | 8 | 8 |
| 0% | 14 | 22 |
| +2% | 18 | 40 |
| +4% | 16 | 56 |
| +6% | 12 | 68 |
| +8% | 10 | 78 |
| +12% | 8 | 86 |
| +18% | 6 | 92 |
| +28% | 4 | 96 |
| +45% | 4 | 100 |
Mean overrun: 7.32 percent. Median overrun: 4.0 percent. 80th percentile: 12 percent. 90th percentile: 18 percent.
The mean is 83 percent higher than the median, driven by eight projects out of a hundred that ran 28 percent or more over. Pearson skew on this distribution is well above 1.5.
Now the two questions a developer actually asks, which have different answers.
"Will 5 percent cover this job?" This is a single-draw question, so read the percentile directly. Cumulative frequency at or below 4 percent is 56, and at or below 6 percent is 68. Five percent covers you roughly 60 percent of the time. That is a coin flip with a slight edge, dressed up as prudence. To cover 80 percent of outcomes you need 12 percent. To cover 90 percent you need 18 percent.
"How much contingency does the program need?" This is a sum, so it is a mean question. Ten projects at $80M of hard cost each is $800M of exposure. A 5 percent contingency funds $40M. The expected overrun across the program is 7.32 percent of $800M, or $58.6M. The program is underfunded by $18.6M.
Here is the trap, and it is not obvious. That $18.6M shortfall never appears as a program-level problem. It appears as capital calls on individual deals, arriving one at a time, each one explained by a specific and entirely genuine cause: an unforeseen condition on the Riverside job, a subcontractor bankruptcy on the Elm Street job, a design change the city forced on the Harbor job. Every explanation is true. The pattern is invisible because each event has a story, and the story is always about that project rather than about the fact that the contingency policy was set from a median-shaped intuition.
Developers set contingency from experience, and experience is a sequence of single draws, which trains the median. Six of your last ten jobs came in under 5 percent. The intuition that 5 percent is a comfortable number is empirically grounded and structurally wrong, because the four jobs that blew through it did so by enough to swamp the six that did not.
The correct policy has two numbers. Carry a project-level contingency set at a percentile that reflects your tolerance for a capital call, typically P75 to P85, which is 8 to 12 percent here. Then hold a program-level reserve sized off the mean, because at the program level the law of large numbers is actually operating and the mean is what you will pay. The two numbers exist for two different reasons and neither substitutes for the other.
Part VII: Household Income, and the Most Expensive Mistake in Market Studies
If you read only one section of this article, read this one, because this specific error has killed more deals than every other item here combined.
A trade area shows:
- Median household income: $78,000
- Mean household income: $104,000
The ratio is 1.333, implying a log-scale dispersion σ of about 0.76, which is very high and which is normal for household income. Income is the most reliably right-skewed variable in the social sciences. A trade area can contain fourteen households earning $2M and it will move the mean without moving the median at all.
Apply the standard 30 percent rent-to-income affordability screen:
- Off the median: $78,000 × 0.30 / 12 = $1,950 per month
- Off the mean: $104,000 × 0.30 / 12 = $2,600 per month
The mean-derived rent is 33 percent higher. A market study that quotes average household income and a pro forma that underwrites $2,600 rents will produce a building that half the trade area is definitionally shut out of, and it will do so with numbers that are internally consistent and technically accurate.
The failure mode is specific and worth naming: the deal will lease. Slowly, at a discount, drawing renters from outside the trade area with a marketing spend nobody underwrote, hitting stabilization nine months late with a concession structure that never fully burns off. It will not fail obviously enough to teach anyone the lesson. It will just quietly earn 400 basis points less than the pro forma, and the post-mortem will blame the market.
Three defenses.
Always demand the median in a market study, and refuse the mean. Census and ACS report both. The median is the standard for income for exactly this reason, and a market study that leads with mean household income is either sloppy or selling.
Ask for the income distribution, not the central tendency. The real question is not what a typical household earns, it is how many households in the trade area can afford your rent. That is a count above a threshold, and it is directly available. At $2,200 in rent, the qualifying income at a 30 percent ratio is $88,000, and the market study should tell you what share of trade-area households clear that. If the answer is 31 percent, you need to know whether 31 percent of that household count is enough to absorb your 300 units against the rest of the pipeline chasing the same 31 percent.
Check the renter-household median specifically, not the all-household median. Renter households have lower median incomes than owner households in essentially every market, often by 35 to 45 percent. Using the all-household median already overstates your renter pool's capacity before anyone touches the mean.
Part VIII: Simpson's Paradox, or How Every Submarket Grew While the Portfolio Shrank
Averages of subgroups can move in the opposite direction from the average of the whole. This is not a curiosity, it is a routine occurrence in any portfolio whose composition is changing, which is all of them.
A portfolio in year one:
| Submarket | Units | Average rent | Total rent |
|---|---|---|---|
| Submarket A | 400 | $2,600 | $1,040,000 |
| Submarket B | 200 | $1,600 | $320,000 |
| Portfolio | 600 | $2,266.67 | $1,360,000 |
Over the year, rents grow 3 percent in both submarkets on a same-store basis. A goes to $2,678, B goes to $1,648. Separately, the firm sells 100 units in A and acquires 300 units in B.
Year two:
| Submarket | Units | Average rent | Total rent |
|---|---|---|---|
| Submarket A | 300 | $2,678 | $803,400 |
| Submarket B | 500 | $1,648 | $824,000 |
| Portfolio | 800 | $2,034.25 | $1,627,400 |
Every submarket grew 3 percent. The portfolio average rent fell 10.2 percent.
Nothing went wrong. Total revenue rose 19.7 percent. The portfolio average fell purely because the mix shifted toward the cheaper submarket, and the portfolio average is a count-weighted number that cannot distinguish a mix shift from a price change.
This is the entire reason the same-store metric exists, and it is why any portfolio-level average rent, average cap rate, average occupancy, or average expense ratio is uninterpretable without knowing whether the composition moved. When someone reports that portfolio average rent declined, the first question is always whether it declined or whether they bought cheaper buildings.
The reverse case is more dangerous because it is flattering. A firm that sells its weakest assets will report rising average rents, rising average occupancy, and a falling average expense ratio, and every one of those improvements can be pure disposition effect with zero operational content. Ask for same-store.
Part IX: The Median Lies Too
Everything so far has been a case for the median. Now the other side, because the median has failure modes that are less discussed and in some ways worse, since the median's reputation for robustness makes people trust it uncritically.
The median is blind to the tail, and the tail is where the outcomes live. Robustness to outliers is the same property as insensitivity to outliers. In real estate, the outliers are not noise. The trophy trade, the 45 percent cost overrun, the asset that goes dark, and the deal that returns 4x are not measurement errors to be trimmed away. They are the events that determine whether a firm compounds or dies. A statistic engineered to ignore them is the wrong statistic for any question about survival or about upside.
A stable median can hide a market being torn in half. Imagine a submarket where the median rent is flat for three years. Underneath, the pre-1985 stock is losing 4 percent a year in real terms while new deliveries are pricing 6 percent higher each year. The distribution is pulling apart into two modes and the median, sitting in the shrinking middle, reports nothing. The mean would have moved. The mean-median ratio would have moved a lot. Watching only the median, you would have missed a structural change in the market you operate in.
The median is censored, and censoring runs the wrong way. Median days on market is computed only over properties that actually sold. In a freezing market, the listings that would have taken 300 days do not sell at all, they get withdrawn, so they never enter the sample. The median days on market can therefore fall while the market deteriorates, because the slow half of the distribution has been removed rather than measured. The same censoring afflicts median lease-up duration, which excludes projects still leasing, and median hold period, which excludes assets nobody will buy. Any median computed over completed events in a distressed environment is measuring survivorship.
The median cannot be aggregated, at all. The median of medians is not the median. If you have median rents for twelve properties, there is no operation that combines them into the portfolio median. You need the underlying distribution. The mean at least has the courtesy of aggregating correctly when weighted.
Part X: The Deepest Version, Which Is About Time
There is one more distinction, and it is the one that separates a fund from a developer.
The arithmetic mean answers the question: if I ran this many times simultaneously, what would the average outcome be? That is an ensemble average. It is the right question for a portfolio of thirty concurrent deals, because you are literally running the ensemble and the law of large numbers will deliver something close to the mean.
But a sponsor doing one deal, then reinvesting the proceeds into the next, is not running an ensemble. They are running a single path through time, and returns compound multiplicatively along it. The relevant statistic is the time average, which is the geometric mean, and the two are not the same number.
Three years of levered equity returns: +50 percent, +50 percent, −60 percent.
Arithmetic mean: (50 + 50 − 60) / 3 = +13.3 percent per year.
Actual outcome: 1.50 × 1.50 × 0.40 = 0.90. You have 90 cents of every dollar. The geometric mean is 0.90^(1/3) − 1 = −3.45 percent per year.
The "average return" is positive 13.3 percent and the investor lost 10 percent of their capital. The gap, 16.8 percentage points a year, is volatility drag, and it is not a rounding error or a technicality. It is the difference between a track record and a wealth outcome.
For moderate volatility there is a useful approximation, geometric ≈ arithmetic − σ²/2, which makes explicit that the drag scales with the square of volatility. Doubling the volatility of a strategy quadruples the drag. Worth noting honestly: that approximation is second-order and breaks down badly at the volatility in this example, where it predicts about −0.1 percent against an actual −3.45 percent. Levered development equity lives at exactly the volatility where the approximation stops working, which is its own argument for computing the geometric mean directly rather than adjusting the arithmetic one.
The practical consequences.
Report the geometric mean of a track record, or report the pooled multiple, and never the arithmetic average of annual returns. The arithmetic average of annual returns is not a number anyone ever received.
A strategy with a higher mean and higher volatility can compound to less than a lower-mean, lower-volatility strategy. This is the entire quantitative case for the boring end of the risk spectrum, and it is why the NCREIF data on multifamily's shallow drawdowns matters more than its headline compound return.
Never risk a fraction of capital that makes the −100 percent path reachable. The geometric mean of any path containing a single total loss is negative infinity, regardless of how spectacular the other years were. An ensemble can absorb a zero. A single path cannot. This is why sizing discipline is not conservatism, it is the only way to be around long enough for the mean to mean anything.
Part XI: The Table
| Question you are asking | Statistic | Why |
|---|---|---|
| Total rent roll, total NOI, total cost, total absorption | Mean | Total = mean × count. Only the mean reconstructs a sum. |
| What will the next unit rent for | Median of that unit type | Single draw, and segment before you summarize. |
| Program-level contingency reserve | Mean overrun | It is a sum across many projects. |
| Project-level contingency | P75 to P85 | It is one draw, and you care about the tail, not the center. |
| Trade-area affordability | Median household income, then the count above your threshold | Income is extremely right-skewed and the mean is not a household. |
| Portfolio cap rate | Value-weighted, or harmonic when NOI is level | Cap rate is a ratio with value in the denominator. |
| Rent per square foot across a rent roll | Weighted by square feet | Ratios never average directly. |
| Fund or track record return | Pooled IRR, or geometric mean | IRRs do not aggregate under any weighting. |
| Comparable sale value conclusion | Adjusted mean, or trimmed mean if you cannot adjust | Median throws away information you paid for. |
| Price index over time | Repeat-sales, never a median | Median price is contaminated by mix. |
| Loss reserve, insurance, cat exposure | Mean of the loss distribution, plus a percentile buffer | Losses aggregate, so you must fund the sum. |
| Whether this is even one market | The mean-to-median ratio | Above roughly 1.15, stop summarizing and segment. |
| Monte Carlo output | Full percentile set, never the mean alone | The reason you ran a simulation was to see the distribution. |
Part XII: How to Report a Number
A practical standard, and the whole discipline of this article compressed into a habit. Never present a central tendency alone. Present six things:
n. How many observations. A median of five comps is a number with an opinion, not a measurement.
Mean and median together. Always both. Their difference is free information about the distribution's shape and costs you nothing to include.
Standard deviation, or better, the interquartile range. Dispersion is not optional. A market at $1,950 with an IQR of $180 and a market at $1,950 with an IQR of $900 require completely different underwriting.
P10 and P90. Where the tails actually sit. This is what people mean when they ask how bad it can get, and it is the number that should size your contingency and your downside case.
The top-decile share. What fraction of the total comes from the top 10 percent of observations. In the rent roll above, the top decile of units, meaning the 12 penthouses plus 8 of the three-bedrooms, produced 23 percent of revenue. That single figure communicates concentration risk faster than any other number available.
The mean-to-median ratio. One number, computed for free from two you already have, that tells the reader whether to trust the mean at all.
Six numbers where the industry currently reports one. It fits on one line of a memo and it is the difference between a summary and a description.
The Point
The median tells you where the market is. The mean tells you which side is heavy.
Neither is a better statistic. They answer different questions, and the entire craft is in knowing which question you are actually asking. Are you funding a total, or pricing a single event? Are you running an ensemble, or walking one path? Will you experience this many times, or once?
The mean is a bet. It is the fair price of a lottery ticket you get to buy repeatedly, and it is the right number when you actually will. The median is a description. It is what happens on a normal Tuesday, and it is the right number when the next event is the only event that matters to you.
What makes real estate hard is that most people in it are doing both at once. A firm is an ensemble and a developer is a path. The fund's contingency policy should be set from the mean, and the project manager's contingency should be set from a percentile. The portfolio's rent growth should be measured same-store, and the leasing agent's price should be set off the segment median. The track record should compound geometrically, and the loss reserve should be funded arithmetically.
Getting this right does not require better data or better models. It requires asking, before every number you write down, whether you are describing a world or funding one. The two answers are different, they diverge exactly in proportion to how skewed the underlying distribution is, and in this asset class the underlying distribution is always skewed.