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113 Math
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113.023 Statistics - Variance, Standard Deviation

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