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Variance & Standard Deviation

Variance tells us how "spread out" our data is.

The Archery Analogy​

  • Low Variance: All your arrows hit in a tight cluster (they are all very close to the mean).
  • High Variance: Your arrows are scattered all over the target.

Python Implementation​

Standard Deviation is just the square root of Variance, and it's easier to read because it's in the exact same units as the original data.

import numpy as np

tight_cluster = [10, 11, 10, 9, 10]
scattered = [0, 20, 5, 25, -2]

print("Tight Cluster Variance:", np.var(tight_cluster))
print("Tight Cluster Std Dev:", np.std(tight_cluster))

print("\nScattered Variance:", np.var(scattered))
print("Scattered Std Dev:", np.std(scattered))