AI Grounds
Open AI Grounds on a desktop
These interactive lessons need a larger screen. Please continue on a desktop or laptop computer.
AI Grounds
These interactive lessons need a larger screen. Please continue on a desktop or laptop computer.
Guided discovery
Move values. See distances become a measure of spread.
Focus a dot and use arrow keys. Shift moves by 10; Home / End moves to 0 / 100.
Subtract the mean, then square each deviation. Longer bars show larger distances.
| Point | Value | Deviation | Distance | Squared |
|---|---|---|---|---|
| A | 42 | -8.0 | 64.0 | |
| B | 46 | -4.0 | 16.0 | |
| C | 48 | -2.0 | 4.0 | |
| D | 50 | 0.0 | 0.0 | |
| E | 52 | +2.0 | 4.0 | |
| F | 54 | +4.0 | 16.0 | |
| G | 58 | +8.0 | 64.0 | |
| Sum of squared deviations | 168.0 | |||
Deviation = value − mean. Negative means left of the mean; positive means right. The bars share a −100 to +100 scale with zero in the center.
Average squared distance.
24.0
168.0 ÷ 7 = 24.0
Measured in squared units.
Spread in the original units.
4.9
√24.0 ≈ 4.9
A typical distance based on squared distances.
These 7 values are the whole population here, so divide by 7. This lesson describes the dataset; it does not estimate spread from a sample.
Standard deviation · preset means are 50; your edits may move the mean.
Mean 50.0; variance 24.0 squared units; standard deviation 4.9 original units.