Finding quartile in Python given mean, std.dev

Question

Given the mean and standard deviation of a normal distribution, how in Python can I determine the quartile of a given point?

E.g.:

• mu = 0.7
• sigma = 0.1

Which quartile is the value 0.75 in, with Python?

I'm after the quartile itself, not the quartile bounds - i.e. a function should take m, s, and val, and return quartile in the range 0 to 3.

Answer 1

You can define your own function to return the quartile order, being 0,1,2 or 3

def normal_quartile(mu, sigma, value):
    quartiles = []
    quartiles.append( mu- 0.675*sigma )
    quartiles.append( mu )
    quartiles.append( mu+ 0.675*sigma )

    for i, q in enumerate(quartiles):
        if value < q:
            return i
    return 3

print( normal_quartile(0.7, 0.1, 0.55) )
print( normal_quartile(0.7, 0.1, 0.65) )
print( normal_quartile(0.7, 0.1, 0.75) )
print( normal_quartile(0.7, 0.1, 0.95) )

results are:

0
1
2
3