Key Terms

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 with known mean μ and known standard deviation, σ, we are sampling with size n, and we are interested in two new RVs: the sample mean, $\bar{X}$. If the size (n) of the sample is sufficiently large, then $\bar{X}$ ~ N(μ, $\frac{\sigma }{\sqrt{n}}$). If the size (n) of the sample is sufficiently large, then the distribution of the sample means will approximate a normal distributions regardless of the shape of the population. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, $\frac{\sigma }{\sqrt{n}}$, is called the standard error of the mean.

Finite Population Correction Factor

adjusts the variance of the sampling distribution if the population is known and more than 5% of the population is being sampled.

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 $\bar{x}$) is $\overline{x}\text{ = }\frac{\text{Sum of all values in the sample}}{\text{Number of values in the sample}}$, and the mean for a population (denoted by μ) is $\mu \text{ = }\frac{\text{Sum of all values in the population}}{\text{Number of values in the population}}$.

Normal Distribution

a continuous random variable with pdf $f(x)\text{ = }\frac{1}{\sigma \sqrt{2\pi }} e^{\frac{–{\text{(}x–\mu )}^2}{2{\sigma }^2}}$, where μ is the mean of the distribution and σ is the standard deviation.; notation: X ~ N(μ, σ). If μ = 0 and σ = 1, the random variable, Z, is called the 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 $\frac{\sigma }{\sqrt{n}}$.

Standard Error of the Proportion

the standard deviation of the sampling distribution of proportions