Stratified Sample — Definition, Formula & Examples
A stratified sample is a sample obtained by dividing the population into non-overlapping subgroups called strata and then randomly selecting members from each stratum. This ensures every subgroup is represented in the final sample.
A stratified sample is the result of a sampling procedure in which the population is partitioned into mutually exclusive, collectively exhaustive strata, and an independent random sample is drawn from each stratum, with sample sizes typically proportional to the stratum's share of the population.
How It Works
First, identify a characteristic that meaningfully divides your population into distinct groups—such as grade level, age range, or income bracket. Next, sort every member of the population into exactly one stratum. Then draw a random sample from each stratum, usually so that each stratum's sample size is proportional to its share of the whole population. Finally, combine all the stratum-level samples into one overall sample for analysis.
Worked Example
Problem: A high school has 1,200 students: 400 freshmen, 300 sophomores, 300 juniors, and 200 seniors. You want a stratified sample of 60 students, proportional to each grade's size. How many students do you sample from each grade?
Step 1: Find each grade's proportion of the population.
Step 2: Multiply each proportion by the desired sample size of 60.
Step 3: Randomly select the required number of students from each grade and combine them.
Answer: Sample 20 freshmen, 15 sophomores, 15 juniors, and 10 seniors for a total stratified sample of 60 students.
Why It Matters
On the AP Statistics exam, you need to identify and design stratified samples in free-response questions about survey methodology. In real-world polling and medical research, stratified sampling reduces sampling error by guaranteeing that key subgroups are proportionally represented rather than left to chance.
Common Mistakes
Mistake: Confusing stratified sampling with cluster sampling. Students sometimes think splitting a population into groups and sampling from each group is the same as cluster sampling.
Correction: In stratified sampling you sample individuals from every stratum. In cluster sampling you randomly select entire clusters and survey everyone within the chosen clusters. The two methods divide the population differently and for different purposes.