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Introductory Business Statistics

Key Terms

Introductory Business StatisticsKey Terms
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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 x ¯  =  Sum of all values in the sample Number of values in the sample x ¯  =  Sum of all values in the sample Number of values in the sample , and the mean for a population (denoted by μ) is μ =  Sum of all values in the population Number of values in the population μ =  Sum of all values in the population Number of values in the population .
Normal Distribution
a continuous random variable with pdf f(x) =  1 σ 2π   e – (x – μ) 2 2 σ 2 f(x) =  1 σ 2π   e – (x – μ) 2 2 σ 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 σ n σ n .
Standard Error of the Proportion
the standard deviation of the sampling distribution of proportions
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