Sampling Methods Math Example 2

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Example 2

hard
A school has 500 students: 200 freshmen, 150 sophomores, 100 juniors, 50 seniors. Design a proportionally stratified sample of 50 students.

Solution

  1. 1
    Total students: 500; sample size: 50; sampling fraction: 50500=0.10=10%\frac{50}{500} = 0.10 = 10\%
  2. 2
    Freshmen: 200×0.10=20200 \times 0.10 = 20 students sampled
  3. 3
    Sophomores: 150×0.10=15150 \times 0.10 = 15 students sampled
  4. 4
    Juniors: 100×0.10=10100 \times 0.10 = 10 students sampled
  5. 5
    Seniors: 50×0.10=550 \times 0.10 = 5 students sampled
  6. 6
    Total: 20+15+10+5=5020+15+10+5 = 50 ✓

Answer

Sample: 20 freshmen, 15 sophomores, 10 juniors, 5 seniors (each grade sampled at 10%).
Proportional stratified sampling maintains the same sampling fraction within each stratum. This ensures the sample mirrors the population's composition, making it representative across the stratifying variable (grade level).

About Sampling Methods

Systematic approaches for selecting a subset of individuals from a population. The main probability methods are: simple random sample (SRS), stratified random sample, cluster sample, and systematic sample. Convenience sampling is a non-probability method that is generally biased.

Learn more about Sampling Methods →

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