# Sampling Distribution

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Sampling Distribution: -The probability distribution of x? is called its sampling distribution. It lists the various values that x? can assume and the probability of each value of x?.

In general, the probability distribution of a sample statistic is called its sampling distribution.

The value of the sample mean for any one sample will depend on the elements that included in that sample. Consequently the sample mean x?, is a random variable. Therefore, like other random variables, the sample mean possesses a probability distribution, which is more commonly called the sampling distribution of x?.

Other sample statistics, such as median, mode, and standard deviation, also possess sampling distribution.

Formula: - Mean of the sampling distribution=µ
Standard deviation of the sampling distribution=σ/√n.

Example: - Assume that the distribution of SAT scores of all examinees is normal with a mean of 1020 and a standard deviation of 153. Calculate the mean and standard deviation of its sampling distribution when the sample size is
1)    16
2)    1000

Solution: - Let µ and σ be the mean and standard deviation of SAT scores of all examinees. Then, from given information,
µ= 1020          and     σ=153

1)    Mean of the sampling distribution=µ= 1020
Standard deviation of the sampling distribution=σ/√n.
=153/√16
=153/4
=38.25

2)    Similarly when n= 1000 then
Mean of the sampling distribution=µ= 1020
Standard deviation of the sampling distribution=σ/√n.
=153/√1000
=4.838