The process of obtaining a sample from a population of data is called sampling. The quantities describing a population are called parameters, and the quantities describing a sample are called statistics.
Sometimes it is very costly to measure population parameters because of its size. So a sample is drawn from the population, and then an inference is made about the population. A sampling plan is the set of rules used to select a sample. One of the most basics sampling plans is the simple random sampling.
A simple random sample is a subset of a larger population so that each element of the population has an equal probability of getting selected in the subset. This kind of sampling is called as simple random sampling.
A random sample can be drawn from a population by arranging a population in sequence and then numbering them and then using a computer-generated random number to choose the sample.
If it is difficult to code all the members of a population, then every kth member of the population is selected. This type of sampling is called systematic sampling. This kind of sampling gives an approximate random sample. Real sampling situations may require us to take an approximate random sample.
A random sample is an unbiased estimator of the population parameters. A sample statistic is a random variable, and the distribution of this random variable (statistic) is called sampling distribution. Both the population as well as the sample statistic have a distribution.
The sampling distribution of a statistic is the distribution of all the distinct values it can assume when it is computed from the samples of the same size randomly drawn from the same population. For example, the sampling distribution of the sample mean. We can take many samples of 30 from a population of 500 and then compute the sample mean of each sample. Then the distribution of different sample means obtained like this is called sampling distribution of the sample mean.
Next LOS: Sampling error
