Numpy Var: A step-by-step Guide with Examples

NumPy is a powerful library in Python for numerical and scientific computing. The 'numpy.var()' function is used to compute the variance of an array or a sequence of numbers. Variance is a measure of the spread or dispersion of data points. Here are step-by-step examples of how to use the 'numpy.var()' function:

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Step 1: Import NumPy

You need to import the NumPy library before using it.


import numpy as np

Step 2: Create a NumPy Array

You can create a NumPy array, which is an efficient data structure for numerical operations, to calculate the variance. Here's an example of creating an array:


data = np.array([10, 20, 30, 40, 50])

Step 3: Calculate Variance

Now that you have your data in a NumPy array, you can use the 'numpy.var()' function to calculate the variance:


variance = np.var(data)

This calculates the population variance by default. If you want to calculate the sample variance, you can specify the ddof (Delta Degrees of Freedom) parameter as 1, like this:


sample_variance = np.var(data, ddof=1)

Step 4: Print the Result

You can print the calculated variance:


print("Population Variance:", variance)
print("Sample Variance:", sample_variance)

Here's the complete code:


import numpy as np

data = np.array([10, 20, 30, 40, 50])
variance = np.var(data)
sample_variance = np.var(data, ddof=1)

print("Population Variance:", variance)
print("Sample Variance:", sample_variance)


Population Variance: 200.0
Sample Variance: 250.0

This code will calculate and print both the population variance and the sample variance of the data array.

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Remember that the 'numpy.var()' function can be used with arrays of any dimension, and it can also calculate the variance along specific axes if you're working with multi-dimensional arrays.

Understand Variance

The variance of a dataset is calculated as the average of the squared differences between each data point and the dataset's mean. The formula for population variance is:

Where:

N is the number of data points.
xᵢ represents each data point.
µ is the mean of the data points.


import numpy as np

data = np.array([10, 20, 30, 40, 50])
mean = np.mean(data)

N = len(data)  # Number of data points
sum_squared_diff = np.sum((data - mean) ** 2)
population_variance = sum_squared_diff / N

print("Population Variance:", population_variance)

Population Variance: 200.0

In this code:

'N' is the number of data points.
'data' - mean calculates the difference between each data point and the mean.
'(data - mean) ** 2' squares these differences.
'np.sum()' calculates the sum of the squared differences.
Finally, you divide the sum by 'N' to get the population variance.

Another Method: Understand Variance


import numpy as np


data = np.array([10, 20, 30, 40, 50])
mean = np.mean(data)
N = len(data)  # Number of data points
squared_diffs = [(x - mean) ** 2 for x in data]  
population_variance = sum(squared_diffs) / N

print("Population Variance:", population_variance)

Population Variance: 200.0

Here's how it works:

N is the number of data points.
The list comprehension [(x - mean) ** 2 for x in data] calculates the squared differences for each data point.
sum(squared_diffs) sums up the squared differences.
Finally, you divide the sum by N to get the population variance.