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Measure of spread
A numerical value that describes how far data values are dispersed (spread out) within a distribution.
Normal distribution
Symmetric distribution, with most values close to the mean and tailing off evenly in either direction. Its frequency graph is a bell-shaped curve.
Population standard deviation (σ)
For a full population of size $n$ with mean $\mu$, the standard deviation is
$$\sigma = \sqrt{\frac{\sum (x-\mu)^2}{n}}$$
Sample standard deviation ($s_{n-1}$)
An estimate of a population’s standard deviation based on a sample of size $n$:
$$s_{n-1} = \sqrt{\frac{\sum (x-\bar{x})^2}{n-1}},$$ where $\bar{x}$ is the sample mean.
Sigma notation (Σ)
A notation meaning “sum of.” For example, $\sum x$ means add all the data values $x$ together.
Standard deviation
The (population) standard deviation is the square root of the variance, that is, the square root of the mean of the squared deviations from the mean. For a population,
$$
\sigma=\sqrt{\frac{\sum(x-\mu)^2}{n}}
$$
Variance
The mean of the squared deviations from the mean. For a population,
$$\sigma^{2}=\frac{\sum(x-\mu)^{2}}{n}$$