Variance

When sampling, it’s not guaranteed to get perfect accuracy, because it’s always possible to get a “weird” sample that skews the results. How many samples to take before we get a justifiable answer? It depends on the variability and underlying possibilities.

Quantifying variation in data: Variance

$variance(X)=\frac{{\sum }_{x\in X}(x-\mu {)}^2}{|X|}$

$\sigma (X)=\sqrt{\frac{1}{|X|}{\sum }_{x\in X}(x-\mu {)}^2}$

• The standard deviation ($\sigma (X)$) is just the square root of the variance.
• Outliers can have a big effect.
• The standard deviation should aways be considered relative to the mean ($\mu$).
• $|X|$ is the cardinality (size) of the set, the number of members in the set.

Squaring the distance means that:

• It doesn’t matter the direction of the difference
• Outliers (big distances) get emphasized.