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Maths Exercices
Identify representative, random, and biased sample

In order to estimate some characteristic within a large group, or population, a smaller group that is a subset of the population, known as a sample, is often used. Samples can be random or biased.

  • A random sample of a population is selected with the goal of finding a representation of the
    entire population without any preference.

  • In a biased sample of a population the sample is chosen with some favoritism.

Let's know more about random samples and biased samples.

Types of Random Samples
Simple Random Sample
A sample that is as likely to be chosen as any other sample from the population. Example. Each student's name is written on a piece of paper. The names are placed in a bowl, and names are picked without looking.
Stratified Random
The population is divided into similar, nonoverlapping groups. Then a simple sample is chosen from each group.  
Systematic Random
Each item is selected according to a specific time or unit interval.  

Types of Biased Samples
Convenience Sample
Any sample that consists of population items that are easily accessed. Example. To represent all the students attending to a school, the principal surveys the students in one math class.
Voluntary Response Sample
A sample which includes only willing participants. Example. Students at a school who wish to express their opinion are asked to complete an online survey.

Robert bought 30 random books from each bookstore in his city. Each bookstore is the same size.
Is this sample of the books in the city likely to be biased?

In a biased sample, some people or items are more likely to be chosen than others.
Since Rogert divided the books into equal-sized groups by bookstore and then chose an equal number of books from each bookstore, it is a representative sample. It is not likely to be a biased sample.