Here is a statistical intuition test from product development guru Donald Reinertsen, apparently based on an example from "Introduction to Probability Theory and its Applications" by William Feller:
Suppose you flip a coin 1000 times. Keep a cumulative sum, starting with zero: every time the coin comes up heads you add 1 to your running total; and every time it comes up tails you subtract 1. How many times will the cumulative sum equal zero? How many flips will there be, on average, between the times the sum equals zero?
The image below is a sparkline simulation of 1,000 coin tosses, as described above. Each pixel on the line represents one toss of the coin: each time a HEAD is tossed, the line moves upwards one pixel; and each time a TAIL is tossed the line moves down one pixel. The whole sparkline represents 1,000 coin tosses - and each time you refresh this page the simulation is re-run, with different random coin tosses.
Did you expect the endpoint to be close to zero every time? Why is it often a long way from zero?
The graph is rendered as an SVG object, which means your browser needs an SVG viewer in order to display it. I think the only browser that doesn't include one by default is IE, for which you may need to install the Adobe SVG plugin or something equivalent.
Coin toss graph
I can't see the graph for some reason?
Can't see the graph?
The graph is rendered as an SVG object, which means your browser needs an SVG viewer in order to display it. I think the only browser that doesn't include one by default is IE, for which you may need to install the Adobe SVG plugin or something equivalent.