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Formula: $s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2}$ for a sample, $\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}$ for a population. Example: The sample standard deviation of 1, 2, 3 is $\sqrt{1} = 1$.

Formula: Middle value of a sorted list or $\frac{1}{2}(middle \, value_1 + middle \, value_2)$ if the list has an even number of observations. Example: The median of 1, 3, 3, 6, 7, 8, 9 is 6.

Formula: $IQR = Q_3 - Q_1$, where $Q_3$ and $Q_1$ are the third and first quartiles, respectively. Example: If $Q_1$ is 25 and $Q_3$ is 75, then $IQR = 75 - 25 = 50$.

Formula: For a random variable $X$, the function $F(x) = P(X \le x)$. Example: If a random variable's PDF is $f(x) = \frac{1}{b-a}$ for $x \in [a, b]$, then $F(x) = \frac{x-a}{b-a}$ for $x \in [a, b]$.

Formula: The value(s) that appear most frequently in the data set. Example: The mode of 1, 2, 4, 4, 5 is 4.

Formula: $\sigma^2 = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})^2$ for a sample, $\sigma^2 = \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2$ for a population. Example: The sample variance of 1, 2, 3 is $(1/2)((1-2)^2+(2-2)^2+(3-2)^2) = 1$.

Formula: For a continuous random variable $X$, the function $f(x)$ such that the probability $P(a \le X \le b) = \int_{a}^{b}f(x)\,dx$. Example: Uniform distribution $U(a,b)$ has PDF $f(x) = \frac{1}{b-a}$ for $x \in [a, b]$.

Formula: $Range = Maximum\ value - Minimum\ value$. Example: The range of 5, 7, 10, 20 is $20 - 5 = 15$.

Formula: $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ are observed values and $E_i$ are expected values. Example: If observed values are 10, 20, 30 and expected values are 15, 15, 30, then $\chi^2 = \frac{(10-15)^2}{15} + \frac{(20-15)^2}{15} + \frac{(30-30)^2}{30} = 3.33$.

Formula: $r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2\sum_{i=1}^{n}(y_i - \bar{y})^2}}$ for a sample. Example: If the covariance is 10, standard deviations are 3 and 2, then $r = 10 / (3 \times 2) = 1.67$ (note that correlation coefficients are between -1 and 1, this is just for illustration).

Formula: $\bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_i$. Example: The mean of 2, 3, 4 is $(2+3+4)/3 = 3$.

Formula: $\sigma_{xy} = \frac{1}{n-1}\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})$ for sample data, $\sigma_{xy} = \frac{1}{n}\sum_{i=1}^{n}(x_i - \mu_x)(y_i - \mu_y)$ for population data. Example: Given two samples (1, 2) and (3, 4), the sample covariance is $(1/1)((1-2)(2-3)+(3-2)(4-3)) = 1$.

Formula: $CV = \frac{s}{\bar{x}} \times 100\%$ (for sample), $CV = \frac{\sigma}{\bar{x}} \times 100\%$ (for population). Example: If the mean is 50 and standard deviation is 5, $CV = (5/50) \times 100\% = 10\%$.

Formula: $P_k = \frac{k}{100}(N+1)$th value for the kth percentile. Example: The 50th percentile (median) of an ordered data list with 9 numbers is the $0.5 \times (9+1) = 5$th number.