# Calculate the Mean and Variance of a Tensor in TensorFlow – TensorFlow Tutorial

By | February 27, 2022

It is very easy to compute the mean and variance of a tensor in tensorflow. In this tutorial, we will introduce how to calculate using tf.nn.moments() function.

If you want to learn how to compute variance and standard deviation in numpy, you can read:

Calculate Average, Variance, Standard Deviation of a Matrix in Numpy

## What is variance?

You can find the definition of variance in this tutorial:

What is Sample Variance and How to Compute it in Numpy – Numpy Tutorial

In tensorflow, we can use tf.nn.moments() function.

## Syntax

tf.nn.moments() is defined as:

tf.nn.moments(
x,
axes,
shift=None,
name=None,
keep_dims=False
)

It will calculate the mean and variance of x

You should notice:

• axes is not the axis
• keep_dims is not the keepdims

## How to use tf.nn.moments()?

We will use some example to show you how to use it.

import numpy as np
import tensorflow as tf

xs = tf.convert_to_tensor(np.array([[[-1,3,2], [-3,1,3]],[[2,-7,4],[5,7, 6]]]), dtype = tf.float32)

fc_mean, fc_var = tf.nn.moments(xs, axes = 2, keep_dims=True)

init = tf.initialize_all_variables()
with tf.Session() as sess:
sess.run(init)
print (sess.run(fc_mean))
print (sess.run(fc_var))

In this  example, xs is a (2,2, 3) tensor, we will compute the mean and variance of it on axes = 2.

Run this code, you will get the value:

[[[ 1.3333334 ]
[ 0.33333334]]

[[-0.33333334]
[ 6.        ]]]
[[[ 2.8888893]
[ 6.222223 ]]

[[22.888887 ]
[ 0.6666667]]]

The shape of mean and variance is [2,2,1], because we set keep_dims=True

How about axes is a list, for example axes = [1, 2]

fc_mean, fc_var = tf.nn.moments(xs, axes = [1, 2], keep_dims=True)

init = tf.initialize_all_variables()
with tf.Session() as sess:
sess.run(init)
print (sess.run(fc_mean))
print (sess.run(fc_var))

You will get this value:

[[[0.8333333]]

[[2.8333333]]]
[[[ 4.805556]]

[[21.805555]]]

if axes = 1

fc_mean, fc_var = tf.nn.moments(xs, axes = [1], keep_dims=True)

init = tf.initialize_all_variables()
with tf.Session() as sess:
sess.run(init)
print (sess.run(fc_mean))
print (sess.run(fc_var))

You will get this value:

[[[-2.   2.   2.5]]

[[ 3.5  0.   5. ]]]
[[[ 1.    1.    0.25]]

[[ 2.25 49.    1.  ]]]

axes determines how to compute the mean and variance of x, you should notice the different feature for x.