- Average
- a number that describes the central tendency of the data; there are a number of specialized averages, including the arithmetic mean, weighted mean, median, mode, and geometric mean.

- Central Limit Theorem
- Given a random variable (RV) with known mean
*Î¼*and known standard deviation,*Ïƒ*, we are sampling with size*n*, and we are interested in two new RVs: the sample mean, $\stackrel{\xc2\xaf}{X}$, and the sample sum,*Î£Î§*. If the size (*n*) of the sample is sufficiently large, then $\stackrel{\xc2\xaf}{X}$ ~*N*(*Î¼*, $\frac{\mathrm{\xcf\u0192}}{\sqrt{n}}$) and*Î£Î§*~*N*(*nÎ¼*, ($\sqrt{n}$)(*Ïƒ*)). If the size (*n*) of the sample is sufficiently large, then the distribution of the sample means and the distribution of the sample sums will approximate a normal distributions regardless of the shape of the population. The mean of the sample means will equal the population mean, and the mean of the sample sums will equal*n*times the population mean. The standard deviation of the distribution of the sample means, $\frac{\mathrm{\xcf\u0192}}{\sqrt{n}}$, is called the standard error of the mean.

- Exponential Distribution
- a continuous random variable (RV) that appears when we are interested in the intervals of time between some random events, for example, the length of time between emergency arrivals at a hospital, notation:
*X*~*Exp*(*m*). The mean is*Î¼*= $\frac{1}{m}$ and the standard deviation is*Ïƒ*= $\frac{1}{m}$. The probability density function is*f*(*x*) = me^{â€“mx},*x*â‰¥ 0 and the cumulative distribution function is*P*(*X*â‰¤*x*) = 1 â€“ e^{â€“mx}.

- Mean
- a number that measures the central tendency; a common name for mean is "average." The term "mean" is a shortened form of "arithmetic mean." By definition, the mean for a sample (denoted by $\stackrel{\xc2\xaf}{x}$) is $\stackrel{\xc2\xaf}{x}\text{\xc2=\xc2}\frac{\text{Sum\xc2of\xc2all\xc2values\xc2in\xc2the\xc2sample}}{\text{Number\xc2of\xc2values\xc2in\xc2the\xc2sample}}$, and the mean for a population (denoted by
*Î¼*) is $\mathrm{\xce\xbc}\text{\xc2=\xc2}\frac{\text{Sum\xc2of\xc2all\xc2values\xc2in\xc2the\xc2population}}{\text{Number\xc2of\xc2values\xc2in\xc2the\xc2population}}$.

- Normal Distribution
- a continuous random variable (RV) with pdf $f(x)\text{\xc2=\xc2}\frac{1}{\mathrm{\xcf\u0192}\sqrt{2\mathrm{\xcf\u20ac}}}\xc2{e}^{\frac{\xe2\u20ac\u201c{\text{(}x\text{\xc2}\xe2\u20ac\u201c\text{\xc2}\mathrm{\xce\xbc})}^{2}}{2{\mathrm{\xcf\u0192}}^{2}}}$, where
*Î¼*is the mean of the distribution and*Ïƒ*is the standard deviation.; notation:*X*~*N*(*Î¼*,*Ïƒ*). If*Î¼*= 0 and*Ïƒ*= 1, the RV is called the**standard normal distribution**.

- Normal Distribution
- a continuous random variable (RV) with pdf $f(x)\text{\xc2=\xc2}\frac{1}{\mathrm{\xcf\u0192}\sqrt{2\mathrm{\xcf\u20ac}}}\xc2{e}^{\frac{\xe2\u20ac\u201c{\text{(}x\text{\xc2}\xe2\u20ac\u201c\text{\xc2}\mathrm{\xce\xbc})}^{2}}{2{\mathrm{\xcf\u0192}}^{2}}}$, where
*Î¼*is the mean of the distribution and*Ïƒ*is the standard deviation; notation:*Î§*~*N*(*Î¼*,*Ïƒ*). If*Î¼*= 0 and*Ïƒ*= 1, the RV is called a**standard normal distribution**.

- Sampling Distribution
- Given simple random samples of size
*n*from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution.

- Standard Error of the Mean
- the standard deviation of the distribution of the sample means, or $\frac{\mathrm{\xcf\u0192}}{\sqrt{n}}$.

- Uniform Distribution
- a continuous random variable (RV) that has equally likely outcomes over the domain,
*a*<*x*<*b*; often referred as the**Rectangular Distribution**because the graph of the pdf has the form of a rectangle. Notation:*X*~*U*(*a*,*b*). The mean is $\mathrm{\xce\xbc}\text{\xc2=\xc2}\frac{a\text{\xc2+\xc2}b}{2}$ and the standard deviation is $\mathrm{\xcf\u0192}\text{\xc2=\xc2}\sqrt{\frac{{(b\xe2\u20ac\u201c\text{a)}}^{2}}{12}}$. The probability density function is $f(x)\text{\xc2=\xc2}\frac{1}{b\xe2\u20ac\u201ca}$ for*a*<*x*<*b*or*a*â‰¤*x*â‰¤*b*. The cumulative distribution is*P*(*X*â‰¤*x*) = $\frac{x\xe2\u20ac\u201c\text{a}}{b\xe2\u20ac\u201c\text{a}}$.