Quick Answer: Standard deviation measures how spread out a set of numbers is from their average. A low standard deviation means most numbers are very close to the average. A high standard deviation means the numbers are widely scattered.
Why the Average is Not Enough
Imagine two cities. City A has temperatures of 70°, 72°, and 68° over three days. City B has temperatures of 100°, 40°, and 70°. Both have the exact same average temperature (70°). But if you pack for a 70° trip to City B, you will freeze and boil. The average hides the extreme variance.
Enter Standard Deviation
Statisticians use standard deviation (often represented by the Greek letter sigma, σ) to solve this. City A has a very low standard deviation because all temperatures are clustered around 70. City B has a massive standard deviation because the data points are wildly spread out.
The 68-95-99.7 Rule
In a normal distribution (a bell curve), standard deviation acts as a magical measuring stick:
- 68% of all data points fall within ONE standard deviation from the mean.
- 95% fall within TWO standard deviations.
- 99.7% fall within THREE standard deviations.
If an event is a "Six Sigma" event (six standard deviations away), it is astronomically rare — roughly a 1 in 500 million chance.