Python - Python Machine Learning - Standard Deviation Part 1: Understanding Standard Deviation

What is Standard Deviation?

Standard deviation (σ) measures the spread of numbers in a dataset. It is calculated as:

σ = √(Σ (xi - x̄)² / N)

Where:

• xi​ is each data point
• xˉ is the mean of the data
• N is the total number of values

Example 1: Calculating Standard Deviation Manually

import math

data = [10, 20, 30, 40, 50]

mean = sum(data) / len(data)  # Calculate mean

variance = sum((x - mean) ** 2 for x in data) / len(data)  # Variance

std_dev = math.sqrt(variance)  # Standard deviation

print("Mean:", mean)

print("Standard Deviation:", std_dev)

Output:

Mean: 30.0

Standard Deviation: 14.142135623730951

Explanation:

We calculate the mean of the dataset.

Then, we find the variance by summing squared differences from the mean.

Finally, we take the square root of the variance to get the standard deviation.