Is that Random?

 A sample is a collection of data from some fraction of a population.  It allows us to learn about the entire population by studying a relatively small portion of the population.  A sample frame is the collection of individuals from which a sample is drawn.

 A census is when every individual in the population is measured.  Not difficult if your population is Mr. Rick’s 7 th period.  Imagine your population is all household in the Commonwealth of Virginia.  What would happen by the them you collected data from the entire population?  Would there be some households that could be easily missed?

 Suppose you are interested in knowing the mean height for everyone in your school. ◦ What would a census tell you? ◦ How close would a sample size of one less student that the population be to the mean of the population? ◦ What about ten less students? ◦ If you took a sample of 100 and another sample of 10, which mean would be closer to the population?

 In general, a larger sample size will result in a more accurate estimate of the population.  When the population is very large, larger samples will not produce significantly better results and are usually more expensive or difficult to obtain.  A balance is usually made, not too small to sacrifice accuracy, and not too large to sacrifice cost.  For very large populations a sample size in the hundreds is normally sufficient.

 Making sure that a sample is truly random means that the person taking the sample has no control over who is selected.  When a sample is not random a bias could appear. This means that some individuals are somehow favored over others in the population.

 A Simple Random Sample (SRS) is the result of a sampling method that assures every possible sample of the same size has an equal probability of being selected.  Describe a method that would ensure your sample of 5 students from this class will be a simple random sample. Compare and discuss your method with others in the class.

 Random Numbers are a primary tool in selecting SRS.  You can get random numbers from your TI- 84 calculator.  Books of random numbers have been published. Page 834  Websites exist which provide truly random numbers.