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.