Lesson 4: Standard Deviation

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Standard deviation ($s$ for a sample, $\sigma$ for a population) is the most powerful measure of spread. It calculates the typical, or "standard," distance that every single data point sits away from the mean.

The calculation requires finding the Variance first (the average of the squared differences from the mean), and then taking the square root to return to the original units.

Sample Standard Deviation Formula:

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Variance is the average of the squared differences from the mean:

Sample variance: $s^2 = \frac{\sum(x - \bar{x})^2}{n-1}$

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Population standard deviation: $\sigma = \sqrt{\frac{\sum(x - \mu)^2}{n}}$

Sample standard deviation: $s = \sqrt{\frac{\sum(x - \bar{x})^2}{n-1}}$

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The shape of a histogram tells a lot about the data distribution.
For many real-world datasets, the graph has a symmetrical bell shape, often referred to as the bell curve or normal distribution.
In a normal distribution, most data values cluster around the center (the mean), with fewer values appearing as you move away from the center in either direction.

Examples