numpy var


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:


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.



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