## What happens if you ask people to pick a number `at random’ between 1 and 100?

I saw this circulating on Twitter and thought I would share it here; it was originally posted on reddit.

The graph shows the results obtained when 6750 people were asked to pick an integer `at random’ between 1 and 100. You might naively expect the histogram to be flat (give or take some Poisson errors), consistent with each number having the same probability of being picked, but there are clearly some numbers that are more likely to be chosen than a constant probability would imply. The most popular picks are in fact 69, 77 and 7 (in descending order).

It’s well known amongst purveyors of conjuring tricks and the like that if you ask people to pick a number between 1 and 10, far more people choose 7 than any other number. And I suppose 77 is an extension of that. More interestingly, however, the top result implies that, given the choice, more people seem to prefer a 69 to anything else…

Anyway, it proves a point that I’ve made more than a few times on this blog, namely that people generally have a very poor idea of what randomness is and are particularly bad at making random choices or generating random sequences.

P.S. Please direct any criticism of the graph (e.g. why the x-axis goes up to 104 or why the x-values are given to two decimal places) to the reddit page…

### 18 Responses to “What happens if you ask people to pick a number `at random’ between 1 and 100?”

1. knudjahnke Says:

And why is 42 not above average? What kind of strange sample was this?

2. Some very unpopular choices in there, too.

• But odd the effect seems much less pronounced in that direction!

3. “More interestingly, however, the top result implies that, given the choice, most people seem to prefer a 69 to anything else…”

We’ll get to the bottom of it eventually.

4. When I was in my late teens I asked myself exactly this question. Wthout actually doing a sample, I decided that the *least* likely number would be 83. So I selected that as the number for my football uniform shirt, which I still have! Looks like I was pretty much on the money!

• telescoper Says:

On what basis did you make this decision?

• Large prime, not associated with any popular concept or common idea. No special relationship between digits (not sequential, not factors, …). Seemed like the most boring number I could think of.

• When Hardy visited Ramanujan in hospital, the former remarked that the registration number of the taxi was an unremarkable number: 1729. Ramanujan immediately said that it is the smallest number which can be written as the sum of two cubes in two different ways.

Where is Ramanujan when you need him? 🙂

https://en.wikipedia.org/wiki/1729_%28number%29

• OK, we have Wikipedia:

83 is:

the sum of three consecutive primes (23 + 29 + 31).

the sum of five consecutive primes (11 + 13 + 17 + 19 + 23).

the 23rd prime number, following 79 (of which it is also a cousin prime) and preceding 89.

a Sophie Germain prime.[1]

a safe prime.[2]

a Chen prime.[3]

an Eisenstein prime with no imaginary part and real part of the form 3n − 1.

a highly cototient number.[4]

• Note that all numbers are interesting. Assume that this is not the case. Then there must be a first non-interesting number. But that fact makes it interesting, so it is not a non-interesting number. Lather, rinse, repeat. Q.E.D.

5. Anton Garrett Says:

Poor old 34. I feel sorry for it.

6. Michel C. Says:

Quote “Anyway, it proves a point that I’ve made more than a few times on this blog, namely that people generally have a very poor idea of what randomness is and are particularly bad at making random choices or generating random sequences.”

It is because ‘randomness’ is the fruit of our imagination. There is no such a thing in nature…

7. It would be interesting to see this graph broken down by gender.

• Old statisticians never die; they just get broken down by age and sex. 😀

8. Toffeenose Says:

It would be particularly interesting to see the gender breakout for those who selected 69…..

• Shouldn’t the distribution be symmetric with respect to a (perhaps the) point?

You probably meant “breakdown”, but “breakout” might work here as well.