# 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, $X – X –$. If the size (n) of the sample is sufficiently large, then $X – X –$ ~ N(μ, $σ n σ n$). 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, $σ n σ n$, 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 $x – x –$) is , and the mean for a population (denoted by μ) is .
Normal Distribution
a continuous random variable with pdf , 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 $σ n σ n$.
Standard Error of the Proportion
the standard deviation of the sampling distribution of proportions