EXERCISE
1Both measure spread, but one speaks your language and the other speaks math's language.
Variance is measured in squared units. If your data is speed in km/h, variance is in km²/h². That is hard to interpret! Standard deviation brings it back to km/h — which your brain can actually understand.
When to use which:
| Metric | Units | Best For |
|---|---|---|
| Variance (σ²) | Squared (km²/h²) | Math formulas, comparing distributions |
| Std Dev (σ) | Original (km/h) | Interpreting spread, explaining to humans |
import numpy
# Temperature in °C
temps = [22.1, 23.4, 21.8, 24.0, 22.5]
var = numpy.var(temps)
std = numpy.std(temps)
print(f"Variance: {round(var, 2)} °C²")
# Output: Variance: 0.57 °C²
print(f"Std Dev: {round(std, 2)} °C")
# Output: Std Dev: 0.76 °C
# "Temperatures vary by about 0.76°C" makes sense
# "Temperatures vary by 0.57 degrees-squared" does not
Practical ML example — comparing feature spreads:
import numpy
heights = [165, 170, 175, 180, 185]
weights = [55, 65, 70, 80, 95]
print(f"Height variance: {numpy.var(heights)}")
# Output: Height variance: 50.0
print(f"Weight variance: {numpy.var(weights)}")
# Output: Weight variance: 170.0
# Weight has MORE spread — this matters when scaling features
Pro Tip: In ML, variance appears in the formula for many algorithms — PCA (Principal Component Analysis) finds the direction of maximum variance, and Bias-Variance tradeoff is one of the most important concepts in model evaluation. You will meet variance again and again throughout your ML journey.