# Sampling Distribution and Statistics

Sampling Distribution of the Sample Mean
10:52 — by Khan Academy

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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. σ by the square root of sample size n. it is also called Standard Error SE of Sampling distribution of Means..

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