Parameters versus Statistics

Return to the Math 160 Chapter 1 Topics page Revised October, 2013

Values derived from populations are called population parameters. Values derived from samples are called sample statistics.

To set the stage for discussing parameters and statistics we will consider the following items:

  1. All of the students in our section of Math 160;
  2. All of the students in all of the sections of Math 160 this term;
  3. All of the students in Math 160 sections taught by Roger Palay since Fall term 1999;
  4. All of the students in any Math section at the college this term;
  5. All of the students in any Math section taught by Roger Palay since Fall term 1999;
  6. All of the students in any credit class at the college this term;
  7. All of the students in any credit Math class in any Michigan community college this term;
  8. All of the students in any credit class in any Michigan community college this term.
In all cases, for the group of students identified, we could find values such as
  1. the group mean age;
  2. the total number of credits earned by students in the group;
  3. the average number of credits earned by students in the group;
  4. the highest age of students in each group;
  5. the average number of credits being taken this term by students in the group.
Each of the items 1 through 5 is a value derived from a group. Each of the items 1 through 5 could be a parameter or a statistic. We cannot tell if it is a parameter or a statistic until we know how we are looking at the group from which it is computed. Thus, if we are looking at the group mean age of all of the students in our Math 160 section and we are looking at that section as a population, then the group mean age is a parameter, because it is a value derived from the population. On the other hand, if we are looking at the group of students in our Math 160 class as a sample of all the students in Math 160 this term, then that same value, the mean age of students in our section, is a statistic of that sample. If we are looking at the average number of credits earned by all of the students in all of the Math 160 sections this term, then that value could be a parameter or a statistic depending upon how we view the group of students in all sections of Math 160 this term. If we are looking at that group as a population, then the average number of credits earned is a parameter of the population. If, however, we are looking at that group as a sample of all the students taking any math class at the college then that value is a statistic of the sample. Either way we compute the value the same way, but we refer to it differently dependeing upon how we are viewing the group, as a population or as a sample of a larger population.

Return to the Math 160 Chapter 1 Topics page

©Roger M. Palay
Saline, MI 48176
October, 2013