There are three kinds of distributions The sampling distribution of the mean for a that we need to distinguish random sample has extremely important properties. As the sample size n increases, Population Distribution: the distribution the sampling distribution of the mean more of scores in a population, for example, the and more closely resembles a normal distribution of height scores for everyone distribution Statisticians refer to this tendency as the Distribution of a Sample: the distribution central limit theorem one of the most of scores in a sample, for example, the height scores of the students in this class mportant ideas in statistics. Sampling Distribution: the distribution of some statistic(e.g, the mean) in all The following figure presents a schematic depiction of these three distributions. It is obviously impossible to actually draw all possible samples Actually the sampling distribution of the mates a normal distribution fairly closely for sample sizes of 30 or more. This is true regardless of the shape of the variable s distribution in the population. Thus even if a variable is not normally distributed in the population, the mean of all possible sample means of this ariable is the same as the population mean,μ5 9 There are three kinds of distributions that we need to distinguish • Population Distribution: the distribution of scores in a population, for example, the distribution of height scores for everyone in a country. • Distribution of a Sample: the distribution of scores in a sample, for example, the height scores of the students in this class. • Sampling Distribution: the distribution of some statistic (e.g., the mean) in all possible samples. 10 The following figure presents a schematic depiction The following figure presents a schematic depiction of these three distributions. It is obviously impossible of these three distributions. It is obviously impossible to actually draw all possible samples 6 11 • The sampling distribution of the mean for a random sample has extremely important properties. As the sample size n increases, the sampling distribution of the mean more and more closely resembles a normal distribution. • Statisticians refer to this tendency as the central limit theorem, one of the most important ideas in statistics. 12 • Actually the sampling distribution of the mean approximates a normal distribution fairly closely for sample sizes of 30 or more. This is true regardless of the shape of the variable’s distribution in the population. Thus even if a variable is not normally distributed in the population, the mean of all possible sample means of this variable is the same as the population mean, μ