Enter Data Set
Uncheck for population data (n denominator)
Data points: 5
Standard Deviation
4.74
Sample (s)
Variance
22.50
Mean
18.00
Minimum
12
Maximum
24
Range
12
68-95-99.7 Rule (Empirical Rule)
68%
within 1σ
13.3 - 22.7
95%
within 2σ
8.5 - 27.5
99.7%
within 3σ
3.8 - 32.2
Understanding Standard Deviation
Standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that values tend to be close to the mean, while a high standard deviation indicates that values are spread out over a wider range.
Sample vs Population
- Sample (s): Use when data represents a sample of a larger population. Uses n-1 denominator.
- Population (σ): Use when data includes all members of the population. Uses n denominator.
Formulas
Sample Variance (s²) = Σ(x - x̄)² / (n - 1)
Population Variance (σ²) = Σ(x - x̄)² / n
Standard Deviation = √Variance
Population Variance (σ²) = Σ(x - x̄)² / n
Standard Deviation = √Variance
Empirical Rule
For normally distributed data:
- 68% of data falls within 1 standard deviation of the mean
- 95% of data falls within 2 standard deviations of the mean
- 99.7% of data falls within 3 standard deviations of the mean