# Sampling Distribution and Statistics

Sampling Distribution of the Sample Mean

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## Key Questions

• The probability distribution of the values of a sample statistic computed from all possible samples of same size is called a sampling distribution.

• The mean of the sampling distribution of sample mean is $\mu$, which is the mean of the population. You could write this as ${\mu}_{\overline{x}} = \mu$.

This will be true for a random sample of size $n$ taken from the same population.

Another way of stating this is that the sample mean $\setminus \overline{x}$ is an unbiased estimator for $\mu$.

One thing this means is that if you take many many random samples of the same size $n$ from the same population, about half the values of $\setminus \overline{x}$ will be larger than $\mu$ and about half will be smaller than $\mu$.

This fact is related to the law of large numbers.

$S D \left(\overline{x}\right) \mathmr{and} S E \left(\overline{x}\right) = \frac{\sigma}{\sqrt{n}}$

#### Explanation:

Standard Deviation of the Sampling distribution of Means can be obtained by dividing the Population s.d. Ïƒ by the square root of sample size n. it is also called Standard Error SE of Sampling distribution of Means..

## Questions

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