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# handout_5_2 - 5.2 The Sampling Distribution of a Sample...

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5.2 The Sampling Distribution of a Sample Mean Figure 5.8 •averages are less variable than individual observations •averages are more normal than individual observations The mean and standard deviation of x

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x = mean of sample, μ = mean of population , σ 2 = population variance select an SRS of size n from a population and measure variable X on each individual in sample the n measurements are values of n random variables- X 1 , X 2 X n EX) Randomly select 100 women from the population and calculate their average height. •X i is measurement on one individual selected at random from population→ then X i has the distribution of the population •if population is large relative to the size of the sample→ X 1 , X 2 X n considered independent Mean and standard deviation of a sample mean Let x be the mean of an SRS of size n from a population having mean μ and standard deviation σ. The mean and standard deviation of x are: x μ = μ x σ = n ●increasing sample size reduces sampling variability Sampling distribution of a sample mean 2
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handout_5_2 - 5.2 The Sampling Distribution of a Sample...

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