xplain which of the following is a statistic and which is a parameter.
a. The mean age of Americans from the 2020 decennial census
b. The unemployment rate for the population of U.S. adults, estimated by the government from a large sample
c. The percentage of students at your school who receive an athletic scholarship
d. The percentage of Arizonans opposed to increasing border control from a poll of 1,000 residents
e. The mean salaries of employees at your school (e.g., administrators, faculty, maintenance)
The correct answer and explanation is :
Let’s go through each item and define whether it is a statistic or a parameter.
a. The mean age of Americans from the 2020 decennial census
- Parameter
Explanation: A parameter is a numerical value that describes a characteristic of the entire population. Since the 2020 decennial census included every individual in the United States (the entire population), the mean age of all Americans is a parameter. The data collected directly from the whole population is considered a parameter because it accurately describes the population.
b. The unemployment rate for the population of U.S. adults, estimated by the government from a large sample
- Statistic
Explanation: A statistic is a numerical value that describes a characteristic of a sample, not the entire population. In this case, the unemployment rate is estimated from a sample of U.S. adults, meaning the data is based on a subset of the population, not the entire population. Therefore, this is a statistic because it represents an estimate based on a sample.
c. The percentage of students at your school who receive an athletic scholarship
- Parameter (if referring to the entire student body)
Explanation: If the percentage is calculated using data from all students at your school (the entire population), it is a parameter because it describes a characteristic of the entire population. If, however, it is based on a subset or sample of students, it would be a statistic.
d. The percentage of Arizonans opposed to increasing border control from a poll of 1,000 residents
- Statistic
Explanation: This is a statistic because it is derived from a sample of 1,000 Arizonans. A statistic describes a characteristic of a sample, and since only 1,000 residents are surveyed (a sample, not the entire population of Arizona), it represents a statistic.
e. The mean salaries of employees at your school (e.g., administrators, faculty, maintenance)
- Parameter (if referring to all employees)
Explanation: If the mean salary is calculated using data from all employees at your school, then it is a parameter because it describes the entire population of employees. If it is based on a sample of employees, then it would be a statistic.
Key Differences:
- Parameter: Describes a characteristic of an entire population (i.e., the full group you’re studying).
- Statistic: Describes a characteristic of a sample, which is only a subset of the population.
In summary, anything that pertains to the entire population (such as the census data or full salary data) is a parameter, while anything derived from a sample (such as a poll or a sample-based estimate) is a statistic.
