Stat Lesson 02: What is a Population, Sample, Statistic, and Parameters?
Population — Collection of all items we are interested in and you want to draw conclusions about.
Population1: All undergraduate students at Purdue University
Population2: All undergraduate students in USA
Sample — Any subset of the population that you use to draw conclusions about the population.
Sample1: Freshmen from population 1
Sample2: A random set of undergraduates from population 1
Sample3: Undergraduates from IVL colleges from population 1
Statistic — A characteristic of a sample (e.g. sample mean)
Parameter — A characteristic of a population (e.g. population mean)
In statistics, we want to know about the population, but it is difficult, if not impossible, to have the whole population at your disposal. (If you have the whole population, there is no uncertainty. You don’t statistics. You just need data analytics) Instead, you draw samples (subsets of the population) and work with it. Based on the sample statistics (e.g. sample mean), you infer the parameters of the population (e.g. population mean).
We must select a random sample from the population to make this inference possible.
In a random sample, every member in the population has the equal opportunity (chance) of being selected.
Let’s say you are doing a customer satisfaction survey. It is not practical to contact every customer, instead you select a random sample of customers and call them to get their feedback. Based on the sample feedback, you infer about the customer satisfaction of the whole customer base. (Caveat — the sample must be random)
Different symbols are used to denote statistics and parameters.
