Key Statistics Terms
Note to the Reader
We assume you are mostly familiar with the basic statistics terms below.
If you are not, this section from OpenStax Introductory Business Statistics is provided for your reference.
In statistics, we generally want to study a . You can think of a population as a collection of persons, things, or objects under study. To study the population, we select a . The idea of sampling is to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population.
Because it takes a lot of time and money to examine an entire population, sampling is a very practical technique. If you wished to compute the overall grade point average at your school, it would make sense to select a sample of students who attend the school. The data collected from the sample would be the students’ grade point averages. In presidential elections, opinion poll samples of 1,000–2,000 people are taken. The opinion poll is supposed to represent the views of the people in the entire country. Manufacturers of canned carbonated drinks take samples to determine if a 16 ounce can contains 16 ounces of carbonated drink. Measurements of the time to fall is another example of a sample: you are doing a few measurements of the infinite number of possible values.
From the sample data, we can calculate a . A statistic is a number that represents a property of the sample. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic. The statistic is an estimate of a population parameter, in this case the mean. A is a numerical characteristic of the whole population that can be estimated by a statistic. Since we considered all math classes to be the population, then the average number of points earned per student over all the math classes is an example of a parameter.
One of the main concerns in the field of statistics is how accurately a statistic estimates a parameter. The accuracy really depends on how well the sample represents the population. The sample must contain the characteristics of the population in order to be a representative sample. We are interested in both the sample statistic and the population parameter in inferential statistics. In a later chapter, we will use the sample statistic to test the validity of the established population parameter.
The complete set of persons, places, things, etc. understudy. Often this set is too large (it may even be infinite) to study in its entirety. As such, we usually sample.
Measuring time, for example, is a sample. You are doing a few measurements of the infinite number of possible values.
A subset of the population under study.
Measuring time, for example, is a sample. You are doing a few measurements of the infinite number of possible values.
A number that represents a property of the sample. Examples could be mean, median, or standard deviation.
A property of the entire population. The average height of all the people on Earth would be a parameter. Parameters are often measured by statistics which are based off samples.
