Section 6.2 Question 1

What is the difference between a sample and a population?

In Section 6.1, we graphed several datasets. In particular, we examined the dividend yields of several companies belonging to the energy sector on the New York Stock Exchange. These companies are a smaller portion of a larger group of companies. Depending on the perspective, they could be considered a smaller part of all companies in the energy sector on the New York Stock Exchange. Or they could be considered a small part of companies on the New York Stock Exchange in general. When we examine a smaller portion of data from a larger set, the smaller portion is called a sample. The sample is selected from a larger set of data called the population.

In statistics, we are often interested in how the numbers we calculate for the sample relate to the numbers we might calculate from the population. Calculating an average from a sample instead of an average from a population may be much convenient and cost effective.

For instance, every day shipping containers enter ports around the United States with parts destined for factories. A single container may contain a huge number of parts. Ideally, every part in the container will be free of defects. However, every container will have a certain proportion of parts that are not usable. It is not cost effective to examine every single part in the container. Instead, a smaller sample is selected from the container. If the proportion of defective parts is too high, the contents of the entire container are rejected. The population is all of the parts in the container and the sample is the smaller group that is selected from this population.

Measures calculated from a sample are called statistics. Measures calculated from a population are called parameters. It is very common for a business to use a small sample of data drawn from a much larger population. Businesses routinely launch products in small test markets to gauge interest. If the product is successful for the sample of consumers in the test market, it might be successful in the larger population of American consumers. The test markets are chosen very carefully to insure the parameters calculated from the sample are reflective of the statistics from the population.