21 Basic Statistics Terminology
Learning Objectives
- Identify the population and sample in a study
- Identify the parameter and statistic in a study
What is Statistics?
The science of statistics deals with the collection, analysis, interpretation, and presentation of data. Data describe characteristics of an individual case such as measurements, genders, survey responses, etc.
Descriptive statistics consist of organizing and summarizing data. Descriptive statistics describe data through numerical summaries, tables, and graphs.
Inferential statistics uses methods that take results from a sample, extends them to the population allowing us to draw conclusions from “good’ data.
Population vs Sample
A population is a collection of persons, things, or objects to be studied. An individual or case is a person or object that is a member of the population being studied. A sample is a portion of the population that is being studied. See the image below for a visual of this relationship.
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Examples: Population vs. Sample
- A food inspector conducts inspections on a randomly selected group of 14 restaurants in Cookeville, Tennessee. Identify the population being studied and the sample chosen.
- Population: all restaurants in Cookeville, Tennessee
- Sample: the 14 restaurants selected
- A factory overseer selects 35 grape flavored candies at random from those produced that week at the factory, then he tests their quality. Identify the population being studied and the sample chosen.
- Population: all grape flavored candies produced that week at the factory.
- Sample: the 35 grape flavored candies selected
Statistic vs Parameter
A statistic is a numerical summary that represents a property of a sample. A parameter is a numerical summary that represents a property of a of a population.
Examples: Statistic vs. Parameter
Examples:
Determine whether the given value is a statistic or a parameter.
- Suppose the percentage of all dog lovers in United States is 74%.
- Solution: 74% is a parameter. It is a measure of the percentage of all dog lovers in the entire US population.
- Suppose a sample of 50 towns in a particular state were surveyed and 64% of the people surveyed were dog lovers.
- Solution: 64% is a statistic. 64% of the sample were dog lovers.
- For each study below, identify both the parameter and the statistic in the study. **See hint below**
- A nutritionist wants to estimate the mean number of calories consumed by children under the age of 8. From a random sample of 350 children under the age of 8, the nutritionist obtains a sample mean of 1,743 calories consumed.
- Solution: The parameter is the mean number of calories consumed by children under the age of 8 (note that the parameter is what the researcher is trying to estimate from the statistic). The Statistic is the sample mean of 1,743 calories consumed.
- A researcher wants to estimate the average farm size in Tennessee. From a simple random sample of 500 farms, the researcher obtains a sample mean farm size of 475 acres.
- Solution: The parameter is the average farm size in Tennessee. The statistic: a sample mean farm size of 475 acres.
- A nutritionist wants to estimate the mean number of calories consumed by children under the age of 8. From a random sample of 350 children under the age of 8, the nutritionist obtains a sample mean of 1,743 calories consumed.
**Hint: Notice how the parameter is what the research wants to estimate. The research estimates this parameter by obtaining a sample and calculating the statistic for the sample!
Variable vs Data
A variable, usually notated by capital letters such as X or Y, is a characteristic or measurement that can be determined for each member of a population. Data are the actual values of the variable. They may be numbers, or they may be words. Datum is a single value.
Examples: Variables and Data
Determine what the key terms refer to in the following study.
- We want to know the average (mean) amount of money first year college students spend at TCC on school supplies that do not include books. We randomly surveyed 100 first year students at the college. Three of those students spent $150, $200, and $225, respectively.
- Population: all first year students at ABC College
- Sample: 100 first year students selected
- Parameter: the average (mean) amount of money first year college students spend at ABC College on school supplies that do not include books
- Statistic: the average (mean) amount of money the 100 selected first year college students spend at ABC College on school supplies that do not include books
- Variable: the amount of money first year college students spend at ABC College on school supplies that do not include books
- Data: $150, $200, and $225
Attributions
- Content and structure adapted from RSCC Math 1410/1420 OER Team, 2022, CC BY 4.0.
- Portions of this content adopted form Openstax ‘Introductory Statistics’: Definitions of Statistics , Probability, and Key Terms (https://openstax.org/books/introductory-statistics/pages/1-1-definitions-of-statistics-probability-and-key-terms )
- Image credits:
- Population/Sample Image: Loneshieling, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
