Distribuciones muestrales (inglés)

Sample Distributions.
The frequency distribution of a sample statistic is called the sampling distribution. Generally, the sampling distribution of a statistic is that of all possible valuescalculated from samples of the same size.
Suppose that you have selected random samples of size 20 in a large population. The Media sample is calculated for each sample x, the collection of all thesesample means is called the sampling distribution of means, which can be illustrated in the next figure:


Suppose that we choose random samples of size 20, a large population, and we calculate thestandard deviation of each one. The collection of all these standard deviations is called the sampling distribution of sample standard deviation, and that we can see it in the next figure:


Example:The samples are selected in order of size 2, with a replacement of the population of values 0, 2, 4 and 6.
Find:

The population mean.
, The population standard deviation.
x, the meanof the sampling distribution of means.
x, the standard deviation of the sampling distribution of means.

Solution:

a. The population mean is:




b. The population standard deviationis:



c. Here are the elements of the sampling distribution of the mean and the corresponding frequency distribution.



The mean of the sampling distribution of means is:

d) Thestandard deviation of the sampling distribution of means is:


With all this we can deduce that:

As for any random variable, the mean distribution sample has an average or expected value,variance and standard deviation can be demonstrated that the sampling distribution of means is equal to half the population means.
That is:


Sample distributions

Having done the exercise above, itshows that a sampling distribution is generated by extracting all possible samples of the same population size, these calculators to your statistics.

If the population from which samples are...