Random Sampling Methods
Class 11 Statistics — Simple Random Sampling, Restricted Random Sampling Methods
Introduction to Random Sampling
Key Takeaways
- Also known as 'Probability Sampling' because selection works on Law of Probability.
- There is no room for discrimination in random sampling.
- Random sample is a replica of the universe; measurements of such a sample estimate the measurements of the population.
- Two methods: (i) Simple Random Sampling; (ii) Restricted Random Sampling.
Simple Random Sampling
Merits and Demerits of Simple Random Sampling
Merits
- No Personal Bias: Every item has equal chance — free from personal bias.
- Based on Probability: Rules of probability are applicable.
- Accuracy can be assessed: Magnitude of sampling errors can be estimated.
- Representative as size increases: As size increases, sample becomes more representative.
Demerits
- ✗Unsuitable for small sampling: If sample is not large, it may not represent the population.
- ✗Difficult to prepare sampling frame: May be difficult for large or infinite population.
- ✗Time Consuming: Numbering population units and preparing slips is time consuming and uneconomical for large populations.
Restricted Random Sampling — The Four Methods
Summary Table — Types of Restricted Random Sampling
| Method | Description | When to Use | Key Limitation |
|---|---|---|---|
| Stratified Random Sampling | Population divided into groups (strata); items taken from each group at random | Heterogeneous population; when representation from all subgroups is needed | Difficult to determine size of strata; may be expensive |
| Systematic Sampling | Every nth item selected from complete list | Complete list available; simple random sampling not feasible | Biased if periodic features exist in data |
| Cluster Sampling | Population divided into clusters; some clusters selected at random | When list of all units is difficult to prepare | Risk of unrepresentative clusters |
| Multistage Sampling | Cluster sampling carried out in multiple stages | Very large populations; when resources are limited | High subjectivity; portions of population cut out |