Calculate the average, variance and standard deviation in Python using NumPy

08 Oct, 2021
Numpy in 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 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,
 
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
# Python program to get average of a list # Importing the NumPy moduleimport numpy as np # Taking a list of elementslist = [2, 4, 4, 4, 5, 5, 7, 9] # Calculating average using average()print(np.average(list))
Output:
5.0
Example 2:
Python
# Python program to get average of a list # Importing the NumPy moduleimport numpy as np # Taking a list of elementslist = [2, 40, 2, 502, 177, 7, 9] # Calculating average using average()print(np.average(list))
Output:
105.57142857142857
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,
 
 
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=<no value>)
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
# Python program to get variance of a list # Importing the NumPy moduleimport numpy as np # Taking a list of elementslist = [2, 4, 4, 4, 5, 5, 7, 9] # Calculating variance using var()print(np.var(list))
Output:
4.0
Example 2:
Python
# Python program to get variance of a list # Importing the NumPy moduleimport numpy as np # Taking a list of elementslist = [212, 231, 234, 564, 235] # Calculating variance using var()print(np.var(list))
Output:
18133.359999999997
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,
 
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=<no value>)
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
# Python program to get# standard deviation of a list # Importing the NumPy moduleimport numpy as np # Taking a list of elementslist = [2, 4, 4, 4, 5, 5, 7, 9] # Calculating standard# deviation using var()print(np.std(list))
Output:
2.0
Example 2:
Python
# Python program to get# standard deviation of a list # Importing the NumPy moduleimport numpy as np # Taking a list of elementslist = [290, 124, 127, 899] # Calculating standard# deviation using var()print(np.std(list))
Output:
318.35750344541907
sagar0719kumar
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