To choose samples, we use sampling and its different types:

In a random or probability sampling, each individual in the population has the same probability to be chosen for the sample.


The different types of random sampling are:
Simple random sampling (the base for the other types of sampling) consists in listing the elements of the population and choosing the n elements of the sample randomly
Systematic random sampling consists in choosing the n elements of the sample k in k where:
Stratified random sampling, also sometimes called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup.
Cluster random sampling. The problem with random sampling methods when we have to sample a population that's scattered across a wide geographic region is that you will have to geographically cover a very large ground in order to get to each of the units you sampled. In cluster sampling, we follow these steps:
       •divide population into clusters (usually along geographic boundaries)
       •randomly sample clusters
       •measure all units within sampled clusters
The number of samples of size n in a population of N individuals is:
–Without replacement: 
–With replacement: Nn
If you make an error in the sampling process, the results of the sample won’t match the population. This error can be:
Random sample error: in order to reduce this error, you must increase the size of the sample
–A systematic error is associated to the process of selection of the sample and it is reduced by improving the selection
Exercise: A library has 5 sections, in each one there is a certain number of books as is shown in the table:
Section 1 2 3 4 5
Books 500 860 1200 700 740
In order to try to estimate the number of books published in Spanish, we want to extract a sample of 5% of the total books by doing a stratified random sampling with the sections as strata. How many books in each section do we have to select?
Solution: 25, 43, 60, 35 and 37 books

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