Standard deviation (Ο) quantifies how spread out data points are from the average. A low standard deviation means data points cluster near the mean; a high standard deviation means they are spread out.
Steps to Calculate
- Find the mean (average)
- Subtract the mean from each data point and square the result
- Average those squared differences (variance)
- Take the square root of the variance
Example
Data: 4, 8, 6, 5, 3. Mean = 5.2. Squared differences: 1.44, 7.84, 0.64, 0.04, 4.84. Variance = 2.96. SD = β2.96 = 1.72.
The 68-95-99.7 Rule
In a normal distribution: 68% of data falls within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean.