# 7.8: Chapter 7 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, $$\overline X$$. If the size ($$n$$) of the sample is sufficiently large, then $$\overline{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$. 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 $$\overline x$$) is $$\overline x =\overline{x}=\frac{\text { Sum of all values in the sample }}{\text { Number of values in the sample }}$$, and the mean for a population (denoted by $$\mu$$) is $$\mu=\frac{\text { Sum of all values in the population }}{\text { Number of values in the population }}$$.
Normal Distribution
a continuous random variable with pdf $$f(x)=\frac{1}{\sigma \sqrt{2 \pi}} e^{\frac{-(x-\mu)^{2}}{2 \sigma^{2}}}$$, where $$\mu$$ is the mean of the distribution and $$\sigma$$ is the standard deviation.; notation: $$X \sim N(\mu, \sigma)$$. If $$\mu = 0$$ and $$\sigma = 1$$, 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