# Variance and Standard Deviation

Sigma

$$\sigma$$

**Variance**. This is the symbol for variance:

$$\sigma^2$$

- To find variance

- Take the first data point and subtract the mean `(-10-10)`

- Then square it `(-10 - 10)^2`

- Then do the same thing for every data point in the set and divide by the number of values in the dataset. E.g.

- $$\frac{(-10-10)^2 + (0-10)^2 + (10-10)^2 + (20-10)^2 + (30-10)^2}{5}$$

- $$\frac{400 + 100 + 0 + 100 + 400}{5}$$

- $$\frac{1000}{5}$$

- $$\sigma^2 = 200$$

- Also called "mean of the squared distance from the mean"

**Standard deviation** measures the spread of data distribution - the typical distance between each data point and the mean.

- Standard deviation gives us a better sense of how far away, on average, we are from the mean.

Standard Deviation is just the **square root of the variance**. Or, square root of sigma squared:

$$\sqrt{200}$$

- Or, in other words, since variance = sigma squared, then standard deviation is simply sigma.

##### Tags:

- statistics