Expected IQ spread on a jury

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There’s been some discussion online lately about how a large difference in IQ makes it difficult for two people to communicate. There have been studies that confirm this effect. The difficulty is not insurmountable, but it takes deliberate effort to overcome.

Someone dismissed this communication difficulty by pointing out that the expected difference in IQ between two individuals is around 17, suggesting that most communication is between people who differ by more than one standard deviation in IQ. But this calculation assumes people are chosen at random, which they usually are not. People tend to live around and work around others of similar intelligence.

However, a jury is a random sample. It’s not a perfect random sample. For one thing, it starts with a random sample of people who are registered to vote, or who have a drivers license, not all individuals. Furthermore, the pool of potential jurors is reduced to a jury through the process of voir dire, which is not random.

For this post I will make the simplifying assumption that a jury is a random sample from a population with normally distributed IQ with standard deviation σ = 15. The mean doesn’t matter here, but you could assume it’s 100 if you’d like.

By symmetry, the expected range of n samples from a normal random variable is twice the maximum. For n = 12 the range is about 3.26σ, which corresponds to nearly 50 IQ points .

This suggests there’s usually a big spread of IQ on a jury. Even if IQ doesn’t measure intelligence, it measures something, and that something varies a lot over 12 people chosen at random [1].

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[1] In case you’re interested in the technical details, the expected range of n samples from a standard normal random variable is given by

where φ and Φ are the PDF and CDF of a standard normal. Multiply this by σ to get the range of a normal random variable with standard deviation σ. As for how to calculate dn, see the next post.

5 thoughts on “Expected IQ spread on a jury”

Gosset

26 May 2026 at 10:32

Hi! Just wondering if you happened to have any links to the alluded to studies?

John

26 May 2026 at 11:55

No, but one study that I’ve seen cited multiple times involved military units. They performed best when the leader wasn’t too much smarter than his unit.

Tom Moertel

26 May 2026 at 14:54

An interesting follow-up: How often do juries contain "communicatively isolated" jurors? We might say that a juror is communicatively isolated when no other person on the jury is within *x* IQ points. If we let *y* be the share of juries that have at least one isolated juror, the graph of *y* vs *x* might be interesting.

Tom Moertel

26 May 2026 at 15:52

Once I asked my earlier question, I couldn’t stop thinking about it. I finally gave up and wrote a small simulation to answer the question. In short, if we require an IQ gap of 1 standard deviation to isolate a juror, then about 2/3rds of juries will have at least one isolated jury. If we require an IQ gap of 2 standard deviations, only about 6% of juries will have an isolated juror.

Here’s my workbook: https://colab.research.google.com/drive/11_Rzu2EYzoxla1mdklmkEthb79jPvofT?usp=sharing

https://colab.research.google.com/drive/11_Rzu2EYzoxla1mdklmkEthb79jPvofT?usp=sharing

David Lindstrom

26 May 2026 at 21:34

If you are on trial, and there are jurors on your jury whose IQ differs from yours by more than 50, is it a jury of your peers?

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John D. Cook, PhD

My colleagues and I have decades of consulting experience helping companies solve complex problems involving data privacy, applied math, and statistics.

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