Standard Deviation Calculator
CaliforniaCalculator.netEnter a data set to compare each value with its mean.
Data and formula
Standard deviation result
Variance4
Mean5
Count8
Median4.5
Range7
Sum40
- Count the 8 values and calculate their sum: 40.
- Divide by 8 to find the mean: 5.
- Subtract the mean from each value, square each deviation, and add them: 32.
- Divide by 8 (N for a population) to get variance 4.
- Take the square root of the variance to get standard deviation 2.
How the values spread around the mean
Each dot is an entered value. The red center line marks the mean, while the blue measurement band covers one standard deviation below and above it. Values farther from the mean contribute more to variance because their deviations are squared. Compare the diagram with the result table to see which observations have the greatest influence on the measured spread.
| Measure | Value |
|---|---|
| Mean | 5 |
| Standard deviation | 2 |
| Mean − 1 standard deviation | 3.000 |
| Mean + 1 standard deviation | 7.000 |
| Values | 2, 4, 4, 4, 5, 5, 7, 9 |
Deviation calculation details
| # | Value | Value - mean | Squared deviation | z-score |
|---|---|---|---|---|
| 1 | 2 | -3 | 9 | -1.5 |
| 2 | 4 | -1 | 1 | -0.5 |
| 3 | 4 | -1 | 1 | -0.5 |
| 4 | 4 | -1 | 1 | -0.5 |
| 5 | 5 | 0 | 0 | 0 |
| 6 | 5 | 0 | 0 | 0 |
| 7 | 7 | 2 | 4 | 1 |
| 8 | 9 | 4 | 16 | 2 |
Results are displayed in 2-3 decimal places only.
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