Simple random sampling is a sample of individuals that exist in a population; the individuals are randomly selected from the population and placed into a sample. This method of randomly selecting individuals seeks to select a sample size that is an unbiased representation of the population. However, it's not advantageous when the samples of the population vary widely.

Stratified random sampling is a method of sampling that involves the division of a population into smaller groups known as strata. In stratified random sampling or stratification, the strata are formed based on members' shared attributes or characteristics. Stratified random sampling is also called proportional random sampling or quota random sampling.

Stratified random sampling is a better method than simple random sampling. Stratified random sampling divides a population into subgroups or strata, and random samples are taken, in proportion to the population, from each of the strata created. The members in each of the stratum formed have similar attributes and characteristics. This method of sampling is widely used and very useful when the target population is heterogeneous. A simple random sample should be taken from each stratum. Stratified random sampling can be used, for example, to sample students’ grade point averages (GPA) across the nation, people that spend overtime hours at work, and the life expectancy across the world.

### Example

Suppose a research team wants to determine the GPA of college students across the U.S. The research team has difficulty collecting data from all 21 million college students; it decides to take a random sample of the population by using 4,000 students.

Now assume that the team looks at the different attributes of the sample participants and wonders if there are any differences in GPAs and students’ majors. Suppose it finds that 560 students are English majors, 1,135 are science majors, 800 are computer science majors, 1,090 are engineering majors, and 415 are math majors. The team wants to use a proportional stratified random sample where the stratum of the sample is proportional to the random sample in the population.

Assume the team researches the demographics of college students in the U.S and finds the percentage of what students major in 12% major in English, 28% major in science, 24% major in computer science, 21% major in engineering, and 15% major in mathematics. Thus, five strata are created from the stratified random sampling process.

The team then needs to confirm that the stratum of the population is in proportion to the stratum in the sample; however, they find the proportions are not equal. The team then needs to resample 4,000 students from the population and randomly select 480 English, 1,120 science, 960 computer science, 840 engineering, and 600 mathematics students. With those, it has a proportionate stratified random sample of college students, which provides a better representation of students' college majors in the U.S. The researchers can then highlight specific stratum, observe the varying studies of U.S. college students and observe the various grade point averages.

### Applications

The same method used above can be applied to the polling of elections, the income of varying populations, and income for different jobs across a nation.