Calculate standard deviation, variance, and mean for population or sample datasets.
| Number (x) | Mean (μ) | Deviation (x - μ) | Squared (x - μ)² |
|---|---|---|---|
| 10 | 18.00 | -8.0000 | 64.0000 |
| 12 | 18.00 | -6.0000 | 36.0000 |
| 23 | 18.00 | 5.0000 | 25.0000 |
| 23 | 18.00 | 5.0000 | 25.0000 |
| 16 | 18.00 | -2.0000 | 4.0000 |
| 23 | 18.00 | 5.0000 | 25.0000 |
| 21 | 18.00 | 3.0000 | 9.0000 |
| 16 | 18.00 | -2.0000 | 4.0000 |
| Sum (Σ) | 192.0000 |
Standard Deviation (s)
5.23723
Population Standard Deviation (σ): Used when you have data for the entire group (e.g., ages of every student in a class). Equation divides by N.
Sample Standard Deviation (s): Used when you have data for only a subset of the group (e.g., ages of 10 random students from a school). Equation divides by N - 1 to correct bias.
Step 1: Find the mean (average).
Step 2: Subtract the mean from each number and square the result.
Step 3: Find the mean of those squared differences (Variance).
Step 4: Take the square root of that.
