How do you find the variance of an array in python?

numpy.var(arr, axis = None) : Compute the variance of the given data (array elements) along the specified axis(if any).

Example :

x = 1 1 1 1 1
Standard Deviation = 0 . Variance = 0

y = 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4

Step 1 : Mean of distribution 4 = 7
Step 2 : Summation of (x – x.mean())**2 = 178
Step 3 : Finding Mean = 178 /20 = 8.9
This Result is Variance.

Parameters :

arr : [array_like] input array.
axis : [int or tuples of int] axis along which we want to calculate the variance. Otherwise, it will consider arr to be flattened (works on all the axis). axis = 0 means variance along the column and axis = 1 means variance along the row.
out : [ndarray, optional] Different array in which we want to place the result. The array must have the same dimensions as expected output.
dtype : [data-type, optional] Type we desire while computing variance.

Results : Variance of the array (a scalar value if axis is none) or array with variance values along specified axis.

Code #1:

import numpy as np 

arr = [20, 2, 7, 1, 34] 

print("arr : ", arr) 

print("var of arr : ", np.var(arr)) 

print("\nvar of arr : ", np.var(arr, dtype = np.float32)) 

print("\nvar of arr : ", np.var(arr, dtype = np.float64)) 

Output :

arr :  [20, 2, 7, 1, 34]
var of arr :  158.16

var of arr :  158.16

var of arr :  158.16

 
Code #2:

import numpy as np 

arr = [[2, 2, 2, 2, 2], 

    [15, 6, 27, 8, 2], 

    [23, 2, 54, 1, 2, ], 

    [11, 44, 34, 7, 2]] 

print("\nvar of arr, axis = None : ", np.var(arr)) 

print("\nvar of arr, axis = 0 : ", np.var(arr, axis = 0)) 

print("\nvar of arr, axis = 1 : ", np.var(arr, axis = 1)) 

Output :

var of arr, axis = None :  236.14000000000004

var of arr, axis = 0 :  [ 57.1875 312.75   345.6875   9.25     0.    ]

var of arr, axis = 1 :  [  0.    77.04 421.84 269.04]

Numpyin Python is a general-purpose array-processing package. It provides a high-performance multidimensional array object and tools for working with these arrays. It is the fundamental package for scientific computing with Python. Numpy provides very easy methods to calculate the average, variance, and standard deviation.

Average

Average a number expressing the central or typical value in a set of data, in particular the mode, median, or (most commonly) the mean, which is calculated by dividing the sum of the values in the set by their number. The basic formula for the average of n numbers x1, x2, ……xn is

Example:

Suppose there are 8 data points,

The average of these 8 data points is,

Average in Python Using Numpy:

One can calculate the average by using numpy.average() function in python.

Syntax: 

numpy.average(a, axis=None, weights=None, returned=False)

Parameters:

a: Array containing data to be averaged

axis: Axis or axes along which to average a

weights:An array of weights associated with the values in a

returned:Default is False. If True, the tuple is returned, otherwise only the average is returned

Example 1:

Python

import numpy as np

list = [2, 4, 4, 4, 5, 5, 7, 9]

print(np.average(list))

Output:

5.0

Example 2:

Python

import numpy as np

list = [2, 40, 2, 502, 177, 7, 9]

print(np.average(list))

Output:

105.57142857142857

Variance

Variance is the sum of squares of differences between all numbers and means. The mathematical formula for variance is as follows,

Where,

 ? is Mean, 

N is the total number of elements or frequency of distribution. 

Example:

Let’s consider the same dataset that we have taken in average. First, calculate the deviations of each data point from the mean, and square the result of each,

Variance in Python Using Numpy:

One can calculate the variance by using numpy.var() function in python.

Syntax: 

numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=)

Parameters:

a: Array containing data to be averaged

axis: Axis or axes along which to average a

dtype:Type to use in computing the variance. 

out: Alternate output array in which to place the result.

ddof: Delta Degrees of Freedom

keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one

Example 1:

Python

import numpy as np

list = [2, 4, 4, 4, 5, 5, 7, 9]

print(np.var(list))

Output:

4.0

Example 2:

Python

import numpy as np

list = [212, 231, 234, 564, 235]

print(np.var(list))

Output:

18133.359999999997

Standard Deviation

Standard Deviation is the square root of variance. It is a measure of the extent to which data varies from the mean. The mathematical formula for calculating standard deviation is as follows, 

Example:

Standard Deviation for the above data,

Standard Deviation in Python Using Numpy:

One can calculate the standard deviation by using numpy.std() function in python.

Syntax: 

numpy.std(a, axis=None, dtype=None, out=None, ddof=0, keepdims=)

Parameters:

a: Array containing data to be averaged

axis: Axis or axes along which to average a

dtype:Type to use in computing the variance. 

out: Alternate output array in which to place the result.

ddof: Delta Degrees of Freedom

keepdims: If this is set to True, the axes which are reduced are left in the result as dimensions with size one

Example 1:

Python

import numpy as np

list = [2, 4, 4, 4, 5, 5, 7, 9]

print(np.std(list))

Output:

2.0

Example 2:

Python

import numpy as np

list = [290, 124, 127, 899]

print(np.std(list))

Output:

318.35750344541907

How do you find the variance in Python?

How do you find the sample variance in Python using NumPy?

How do you find the standard deviation of an array in Python?

How do you find the variance of a list?