How to play
- A normal (bell) curve appears for 3 seconds — or, in Data mode, a histogram of 150 random values drawn from it, for 5 seconds.
- It disappears. Drag the two sliders to recreate it: the mean moves the centre, the standard deviation sets the spread.
- Lock in. You score up to 10 points for how much your curve overlaps the real one. Five rounds make a game.
In 2-player mode you both memorize the same curve, then take turns guessing privately. The closer curve wins the round — and the game is won on total points.
How scoring works
Your score is the overlapping coefficient: the area that your curve and the real curve share, a standard measure of how similar two distributions are. Identical curves share 100% and score 10.0. For two curves with the same standard deviation σ whose means are d apart, the overlap is 2Φ(−d / 2σ): with σ = 10, being 5 off the mean still scores 8.0, but 10 off scores 6.2 and 20 off only 3.2. Getting the spread right matters just as much as the centre.
Tips from statistics
- The bend points give away the spread. A normal curve changes from bending down to bending up at exactly one standard deviation either side of the mean.
- Height and width trade off. The area is always 1, so a narrow curve is tall and a wide curve is flat. If you remember the peak height, you remember σ.
- In Data mode, expect noise. 150 values never trace the curve perfectly — you are estimating the distribution from a sample, which is exactly what statistics is about. See it in the CLT simulator and the distribution explorer.
Frequently asked questions
Each round scores the overlap between your curve and the real one: the area the two normal distributions share. Identical curves overlap 100% and score 10 points; curves with no overlap score 0. Five rounds give a maximum of 50.
It is the area under the minimum of two probability density curves, a standard measure of how similar two distributions are. For two normal curves with the same standard deviation, it equals 2 times Phi of minus the distance between the means divided by twice the standard deviation.
Yes. A normal curve bends from curving down to curving up at exactly one standard deviation either side of the mean, and about 68% of the area lies between those two points.
Yes. In 2-player mode both players memorize the same curve, then take turns recreating it privately. The closer curve, the one with more overlap, wins the round.