1.14:
Stratified Sampling Method
The stratified sampling method is commonly used while studying a heterogeneous population—a population with large variations.
Here, the population is divided into two or more subgroups or strata with shared characteristics—in this case, a common color. Each stratum represents a homogenous group for the shared character.
Strata are mutually exclusive—that means a subject must be present in only one stratum, like red must be present in only stratum 1. They must also be exhaustive—meaning all subjects with the shared characteristics, in this case all the balls of the same color, must be present in a single stratum.
Then, a few subjects are randomly drawn from each stratum and combined to form a sample.
For example, suppose one wants to know the average weight of students from classes 7 to 12. Since the population has students of different age groups, the weight varies greatly within the population.
So, students are divided into two strata. Then, students are randomly drawn from each stratum to form the sample, and the average weight is calculated.
1.14:
Stratified Sampling Method
Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a stratified sample, divide the population into groups called strata and then take a proportionate number from each stratum. For example, you could stratify (group) your college population by department and then choose a proportionate simple random sample from each stratum (each department) to get a stratified random sample. To choose a simple random sample from each department, number each member of the first department, number each member of the second department, and do the same for the remaining departments. Then use simple random sampling to choose proportionate numbers from the first department and do the same for each of the remaining departments. Those numbers picked from the first department, picked from the second department, and so on represent the members who make up the stratified sample.
A survey of geographical regions can be done using stratified sampling where regions with similar habitat, elevation, and soil type can be divided into strata. Stratified random sampling can also be used to study elections' polling, people who work overtime hours, life expectancy, the income of varying populations, and income for different jobs across a nation.
This text is adapted from Openstax, Introductory Statistics, Section 1.2 Data, Sampling, and Variation in Data and Sampling