Question

A data set gives the ages at death for each of the 38 past presidents of the United States now deceased. a. Is this data set a population or a sample? b. What is the variable being measured? c. Is the variable in part b quantitative or qualitative?

Short answer

Answer: The data set is a population, the variable being measured is the age at death for each past president, and the variable is quantitative.

Step-by-step solution

a. Population or Sample

This data set represents the ages at death for all 38 past U.S. presidents who are deceased. Since it includes data for the entire group of interest (all deceased U.S. presidents), this data set is considered a population.

b. Variable Being Measured

The variable being measured in this data set is the age at death for each past president of the United States.

c. Quantitative or Qualitative Variable

Age at death is a numerical measurement, which means it is a quantitative variable.

Key concepts

Population and Sample

In statistics, one of the first distinctions to understand is between a population and a sample. When you're studying a group, a **population** involves the entire group of interest. In our exercise, the data set lists ages at death for all deceased U.S. presidents. Since it contains information on the entire set of individuals we want to understand, it qualifies as a population.
In many cases, though, researchers deal with a sample instead. A **sample** is a smaller group selected from the population, used to make inferences about the whole group. Samples are generally used when it is impractical or impossible to collect data from everyone in a population.
Choosing between using a population or a sample depends on the resources available and the scope of the research. For comprehensive studies like a census, populations are ideal. For everyday scientific studies, samples often make more practical sense.

• **Population**: Entire group of interest
• **Sample**: Subset of the population

Quantitative Variables

When we look at data, distinguishing between types of variables is crucial. These variables can be classified into two main categories: quantitative and qualitative. In this case, we are dealing with **quantitative variables**.
Quantitative variables are numerical. They can be measured and computed mathematically. For example, the age at death of each deceased U.S. president in our data set is a quantitative variable. Quantitative data allows for a range of mathematical operations to be conducted, such as finding an average or standard deviation.
Unlike qualitative variables, which describe categories or qualities, quantitative variables provide numerical results.
Some examples of quantitative data include:

• Height
• Age
• Test scores

Data Analysis

Analyzing data is an essential step to extract meaningful insights and make informed decisions. In the context of our exercise, data analysis would involve examining the ages at death to discern patterns or averages among U.S. presidents.
Data analysis often starts with descriptive statistics, which summarize the main characteristics of the data, such as the mean, median, and mode. Understanding these basic statistics helps to get an overview of the data trend.
For the ages at death, you might compute:

• **Mean** (average age at death)
• **Median** (middle value if ages were listed in order)
• **Range** (difference between the youngest and oldest age at death)

From there, further statistical analysis can be carried out to understand deeper relationships or comparisons. The ultimate goal of data analysis is to transform raw data into insights that can guide future actions or research.