Understanding Variables for Sampling Methods

The question asks about the type of variable used when you divide a large group (a universe of 500 students) into smaller subgroups based on a specific characteristic (gender) and then take a random sample from each of those subgroups. This specific method of sampling is known as stratified sampling.

What is Stratified Sampling?

Stratified sampling is a technique where a population is divided into distinct subgroups, called strata, based on certain shared characteristics. After dividing the population into strata, a random sample is then selected from each stratum. The goal is often to ensure that each subgroup is represented in the sample in proportion to its size in the population, or sometimes to oversample smaller groups.

Identifying the Correct Variable

In the context of stratified sampling, the characteristic used to divide the population into strata is referred to as the stratification variable or stratified variable. In this question, the population of 500 students is being divided based on their gender. Therefore, gender is the characteristic defining the subgroups (males and females).

Let's look at the given options:

• Control variable: A control variable is something kept constant or accounted for to prevent it from influencing the relationship between the independent and dependent variables in an experiment. This concept is related to experimental design, not the variable used for dividing a population for sampling.
• Independent variable: An independent variable is the variable that is changed or manipulated in an experiment to see its effect on the dependent variable. This is also related to cause-and-effect studies, not the characteristic used for stratification in sampling.
• Dependent variable: A dependent variable is the variable being measured or observed in an experiment to see if it is affected by the independent variable. Like the independent variable, it's a concept from experimental research design.
• Stratified variable: This is the variable used to divide a population into strata (subgroups) before sampling. In the scenario described, the population is divided by gender. Thus, gender acts as the stratified variable.

Based on the definitions and the description in the question, the variable used to divide the 500 students by their gender for taking random samples from each group is the stratified variable.

The process described involves:

1. Identifying the population: 500 students.
2. Choosing the stratification variable: Gender.
3. Dividing the population into strata based on the variable: Males and Females.
4. Taking a random sample from each stratum.

This clearly aligns with the definition and purpose of a stratified variable in stratified sampling.

Revision Table: Types of Variables

Additional Information: Why Stratified Sampling?

Stratified sampling is used for several reasons:

• It ensures that key subgroups within the population are represented in the sample.
• It can lead to more precise estimates than simple random sampling, especially if the characteristic used for stratification is related to the variable being studied.
• It allows for separate analysis of each stratum, which might be important for understanding differences between subgroups.

In the example of students and gender, researchers might use stratified sampling to ensure they have enough male and female students to compare opinions or characteristics between genders, or simply to get a sample that accurately reflects the gender distribution of the 500 students.