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Probability & Statistics

Distributions

Variance & Standard Deviation

7 min+65 XPStep 1/10

Same average, different worlds

Two cities both average 72°F. In one it's 70–75°F every single day; in the other it swings from 40°F to 110°F. Same mean — unrecognizably different lives.

Variance measures how far typical values wander from the mean: the average squared distance. Its square root, the standard deviation, returns the units, so 'a 10-point SD' means something in the original scale.

  • Small SD → data hugs the mean, predictable
  • Large SD → values are all over the map, and the mean describes nobody

warning

An average without a spread is half a measurement. 'Average wait: 5 minutes' means very different things if the SD is 30 seconds or 20 minutes.