Lesson 2 of 9
Dispersion
Two US sectors with almost the same average P/E have very different spreads. The average alone hides the fact that would change how you read a company.
By Javier Sanz
Founder of ValueScreener. Built Ninety Nine, a securities services provider, and sold it to a tier-one global bank; ran operations and internationalization at Alpaca, the brokerage API.
Who writes thisEditorial processLinkedIn (opens in a new tab)X (opens in a new tab)
In one minute
- Variance is the average squared distance from the mean. Standard deviation is its square root, back in the original units.
- Two cohorts with the same average can have completely different spreads, and the spread changes what the average is worth.
- A standard deviation on a skewed distribution is a real number that does not mean what the symmetric intuition says it means.
An average on its own is a single point standing in for a whole cohort. Whether it stands in well depends entirely on how tightly the cohort sits around it, and that is a second number nobody quotes.
Average P/E and its spread, by US sector
- Utilities, 67 listings: mean22.94x
- Utilities: standard deviation13.11x
- Consumer Defensive, 98 listings: mean24.94x
- Consumer Defensive: standard deviation17.21x
Computing it
Take each value's distance from the mean, square it, average the squares, and take the square root. Squaring is what stops the positive and negative distances cancelling to zero, and the square root is what returns the answer to the units you started in.
A sector mean of 22.94 with a standard deviation of 13.11 says the typical company in that cohort sits about thirteen points of P/E away from the middle. That is not a small distance relative to a mean of 23.
Two sectors, two different claims
What a standard deviation does not mean here
The familiar rules of thumb, that about two thirds of a cohort sits within one standard deviation and about 95 percent within two, hold for a symmetric distribution. This one is not symmetric, as the probability course measured, so those rules do not apply.
Specifically, "two standard deviations below the mean" for Technology is 35.11 minus 46.84, which is a negative P/E and therefore not a place any company can be. The arithmetic is fine and the interpretation is meaningless. A statistic can be correctly computed and still be the wrong summary for its data.
When spread is the finding
Two cases where the spread is more informative than the average.
Comparing two cohorts. Utilities at 22.94 and Consumer Defensive at 24.94 look like a two point difference. Next to spreads of 13 and 17 that gap is small enough to be nothing, which the next lesson makes precise.
Judging a single company's place. Three points above a cohort mean means something different when the spread is 5 than when it is 23. Without the second number the first is not interpretable at all.
Check yourself
Two sector cohorts have means of 22.94 and 24.94, with standard deviations of 13.11 and 17.21. What does the two point difference in means tell you?
- That the second sector is more expensive
- Very little, because the gap is small next to the spread within each cohort
- That the second cohort is larger
Show the answer
Answer: B.
A difference has to be read against the variation it sits inside. Two points against spreads of 13 and 17 is well within the ordinary scatter of either group.Why is each distance from the mean squared before averaging?
- To make large distances count more
- Because positive and negative distances would otherwise cancel to zero
- To convert the result into a percentage
Show the answer
Answer: B.
The distances from a mean always sum to zero by construction. Squaring removes the sign so the average measures magnitude, and the square root returns it to the original units. That squaring does also weight large distances more, which is a consequence rather than the purpose.Two standard deviations below the Technology cohort's mean is a negative P/E. What does that show?
- That the standard deviation was computed wrongly
- That symmetric rules of thumb do not apply to a skewed distribution
- That some technology companies have negative P/E ratios
Show the answer
Answer: B.
The computation is correct. The interpretation borrowed from the normal distribution is not, because this cohort has a floor at zero and a long right tail.Sources
- Sector means and standard deviations computed across active US equity listings with a positive P/E below 100, read from this product's own store on 16 September 2026. Cohort sizes are printed in the table.
What this leaves out
- The cohorts here are restricted to listings with a positive ratio below 100, so the extreme right tail is cut before the mean and standard deviation are computed. Without that cut both figures would be dominated by a handful of rows, which is the subject of the fat tails lesson.
- These count listings, not deduplicated companies, and they are not the same cohorts as the published distributions.
- Sector labels come from the stored classification of each listing and a company can be defensibly placed in more than one.
- Nothing here is advice about any security.