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Variance of Numpy Array with NaN Values

The Numpy library in Python comes with a number of useful built-in functions for computing common descriptive statistics like mean, median, standard deviation, etc. In this tutorial, we will look at how to get the variance of values in a Numpy array containing one or more NaN values.

Can you use the numpy.var() function on an array with NaN values?

We use the numpy.var() function to get the variance of values in a Numpy array. But what happens if the array contains one or more NaN values?

Let’s find out.

import numpy as np

# create array
ar = np.array([1, 2, np.nan, 3])
# get array variance
print(np.var(ar))

Output:

nan

Here, we created a one-dimensional Numpy array containing some numbers and a NaN value. We then applied the numpy.var() function which resulted in nan. This happened because the numpy.var() function wasn’t able to handle the nan value present in the array when computing the variance.

Thus, you cannot use the numpy.var() function to calculate the mean of an array with NaN values.

How to ignore NaN values when calculating the variance of a Numpy array?

get variance of numpy array with nan values

You can use the numpy.nanvar() function to calculate the variance of a Numpy array containing NaN values. Pass the array as an argument.

The following is the syntax –

# variance of array with nan values
numpy.nanvar(ar)

It returns the variance among all the values in the array ignoring all the NaN values.

Let’s look at some examples of using the numpy.nanvar() function.

Example 1 – Variance of one-dimensional array with NaN values

Let’s apply the numpy.nanvar() function on the same array used in the example above.

# create array
ar = np.array([1, 2, np.nan, 3])
# get array variance
print(np.nanvar(ar))

Output:

0.6666666666666666

We get the variance in the above array as approximately 0.67. The numpy.nanvar() function ignores the NaN values when computing the variance.

Example 2 – Variance of multi-dimensional array with NaN values

The numpy.nanvar() function is very similar to the numpy.var() function in its arguments. For example, use the axis parameter to specify the axis along which to compute the variance.

First, let’s create a 2-D Numpy array.

# create 2-D numpy array
ar = np.array([[1, np.nan, 3],
               [np.nan, 5, np.nan]])
# display the array
print(ar)

Output:

[[ 1. nan  3.]
 [nan  5. nan]]

Here, we used the numpy.array() function to create a Numpy array with two rows and three columns. You can see that there are some NaN values present in the array.

If you use the Numpy nanvar() function on an array without specifying the axis, it will return the variance of the values inside the array.

# variance of array
print(np.nanvar(ar))

Output:

2.6666666666666665

We get the variance of all the values inside the 2-D array.

Use the numpy.nanvar() function with axis=1 to get the variance for each row in the array.

# variance of each row in array
print(np.nanvar(ar, axis=1))

Output:

[1. 0.]

We get the variance of each row in the above 2-D array. The variance of values in the first row is 1 and the variance of values in the second row is 0.

Use the numpy.nanvar() function with axis=0 to get the variance of each column in the array.

# variance of each column in array
print(np.nanvar(ar, axis=0))

Output:

[0. 0. 0.]

We get the variance of each column in the above 2-D array. In this example, each column has one NaN value and one non-NaN value (thus we get 0 as the variance as there’s only one unique value in the column).

Summary – Variance of Numpy array with NaN values

The following is a short summary of the important points mentioned in this tutorial.

  1. Using the numpy.var() function on an array with NaN values results in NaN.
  2. Use the numpy.nanvar() function to get the variance of values in an array containing one or more NaN values. It computes the variance by taking into account only the non-NaN values in the array.
  3. Similar to the numpy.var() function, you can specify the axis along which you want to compute the variance with the numpy.nanvar() function.

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Author

  • Piyush is a data scientist passionate about using data to understand things better and make informed decisions. In the past, he's worked as a Data Scientist for ZS and holds an engineering degree from IIT Roorkee. His hobbies include watching cricket, reading, and working on side projects.