# Observations needed to estimate standard deviation

I was curious as to practically how well standard deviation can be estimated at different numbers of observed samples. I thought the plot was interesting, so figured I’d share.

Here is the Julia code I used:

```
using Distributions
using Gadfly
function std_of_sample(n)
std(rand(Normal(2, 5), n))
end;
nmax = 200
n_observations = collect(0:nmax * 100) % nmax + 2;
p = plot(
x=n, y=map(std_of_sample, n_observations),
Guide.XLabel("Number of observations"),
Guide.YLabel("Estimated σ"),
Theme(default_color=color("black")),
Coord.Cartesian(ymin=-3, ymax=13, xmin=-20, xmax=220),
Guide.xticks(ticks=[0, 10, 25, 50, 100, 200])
);
draw(PNG(640px, 480px), p)
```

We just sample a different number of samples from a normal distribution with mean 2 and known standard deviation 5.