Implementation of Mean, Variance, and Standard Deviation

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In this section, we will implement the calculations of mean, variance, and standard deviation using Python's NumPy library. This practical example will help you understand how to apply these statistical concepts to actual datasets.

Mean

The mean is a measure that represents the central or typical value in a dataset. It is calculated by summing all the values and dividing by the count of those values.

Mean in Python Using NumPy

You can calculate the mean using the numpy.average() function:

import numpy as np

# Dataset
data = [2, 4, 4, 4, 5, 5, 7, 9]

# Calculating mean
mean = np.average(data)
print("Mean:", mean)  # Output: 5.0

Variance

Variance measures the dispersion of data points from the mean, indicating how much the values in a dataset differ from the mean.

Variance in Python Using NumPy

To calculate variance in Python, use the numpy.var() function:

# Calculating variance
variance = np.var(data)
print("Variance:", variance)  # Output: 4.0

Standard Deviation

Standard deviation is the square root of the variance and indicates the extent to which data varies from the mean.

Standard Deviation in Python Using NumPy

You can calculate the standard deviation using the numpy.std() function:

# Calculating standard deviation
std_deviation = np.std(data)
print("Standard Deviation:", std_deviation)  # Output: 2.0

Full Implementation Example

Here’s how the complete implementation looks:

import numpy as np

# Dataset
data = [2, 4, 4, 4, 5, 5, 7, 9]

# Calculating mean
mean = np.average(data)
print("Mean:", mean)  # Output: 5.0

# Calculating variance
variance = np.var(data)
print("Variance:", variance)  # Output: 4.0

# Calculating standard deviation
std_deviation = np.std(data)
print("Standard Deviation:", std_deviation)  # Output: 2.0

This Python implementation demonstrates how easily you can compute mean, variance, and standard deviation using NumPy, making it a valuable tool for data analysis in machine learning and other scientific applications.

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