Question

Implement a simulation that could answer this question: http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e8d43940b8b543d42104b95

Answer 1

One thing that's interesting, the average pops out of nowhere. A simulation of this would basically be 100 random numbers, but that doesn't account for people's biases. Maybe there's some gnarly calculus that could do better.

Answer 2

I'm doing some research online about that problem and have come to find some conclusions about numbers people choose that could help implement a simulation, and how I would probably do it.

1. It seems people tend to avoid numbers with single digits.
2. It seems people tend to avoid numbers that end with 0.
3. It seems people tend towards numbers closer to 30-80 (still a big range).
4. It seems numbers highly tend to contain a 7.
source: http://www.metafilter.com/54318/random1100
source: http://scienceblogs.com/cognitivedaily/2007/02/is_17_the_most_random_number.php

Of course, all of this isn't absolute.

However I would probably go about this problem:
- generate a random value 1-100
- check the value of the number,
if single digit, accept it with a certain probability (40%?)
if ends in 0, accept it with a certain probability (60%?)
if outside range 30-80, accept it with a certain probability (85%?)
if its rejected, generate another number and try again.

It's probably how I would work about it, but not sure if it could work. Any idea what's the expected output?

Answer 3

My answer tends slightly higher than the one on that link (theirs: 33.3, mine: 35.85), I'm using a kind of algorithm I explain in a previous post, though my probabilities are rather arbitrary. I'll include my code if you'd like to play around with it.