# Calculating Covariance with Python and Numpy

## Calculating Covariance with Python and Numpy

When `a` and `b` are 1-dimensional sequences, `numpy.cov(a,b)` is equivalent to your `cov(a,b)`.

The 2×2 array returned by `np.cov(a,b)` has elements equal to

``````cov(a,a)  cov(a,b)

cov(a,b)  cov(b,b)
``````

(where, again, `cov` is the function you defined above.)

Thanks to unutbu for the explanation. By default numpy.cov calculates the sample covariance. To obtain the population covariance you can specify normalisation by the total N samples like this:

``````numpy.cov(a, b, bias=True)
``````

or like this:

``````numpy.cov(a, b, ddof=0)
``````

#### Calculating Covariance with Python and Numpy

Note that starting in `Python 3.10`, one can obtain the covariance directly from the standard library.

Using `statistics.covariance` which is a measure (the number youre looking for) of the joint variability of two inputs:

``````from statistics import covariance

# x = [1, 2, 3, 4, 5, 6, 7, 8, 9]
# y = [1, 2, 3, 1, 2, 3, 1, 2, 3]
covariance(x, y)
# 0.75
``````