Calculate the 3rd standard deviation for an array

Question

Say, I have an array:

import numpy as np

x = np.array([0, 1, 2, 5, 6, 7, 8, 8, 8, 10, 29, 32, 45])

How can I calculate the 3rd standard deviation for it, so I could get the value of +3sigma as shown on the picture below?

Typically, I use std = np.std(x), but to be honest, I don't know if it returns the 1sigma value or maybe 2sigma, or whatever. I'll very grateful for you help. Thank you in advance.

Answer 1

NumPy's std yields the standard deviation, which is usually denoted with "sigma". To get the 2-sigma or 3-sigma ranges, you can simply multiply sigma with 2 or 3:

print [x.mean() - 3 * x.std(), x.mean() + 3 * x.std()]

Output:

[-27.545797458510656, 52.315028227741429]

For more detailed information, you might refer to the documentation, which states:

The standard deviation is the square root of the average of the squared deviations from the mean, i.e., std = sqrt(mean(abs(x - x.mean())**2)).

http://docs.scipy.org/doc/numpy/reference/generated/numpy.std.html