## Lesson goal: A list of numbers: Checking the standard deviation

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The standard deviation is a measure of how much a group of numbers that have a bell-shaped (or Gaussian, or normal distribution) vary around their average. It is defined as $$\sigma=\sqrt{\frac{1}{N-1}\Sigma (x_i-{\bar x})^2}$$ It tells us if the data has a Gaussian distribution, then 68% of the numbers should fall between the ${\bar x}-\sigma$ and ${\bar x}+\sigma$. Let's see if this holds for the data set we're using here.