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Stratified Sampling

Samples separately from groups so each group is represented.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Randomness & Sampling
Difficulty: Beginner
Family: Sampling Design
Tier: Core
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 6
Code example: Ready
Visualization: Ready

Overview

Stratified Sampling divides a population into strata and draws samples from each stratum to reduce imbalance or variance.

Core Concepts

sample selectionrandom drawstate estimatesampling designrandom sourcedistribution shape

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(n)

Average

O(n)

Worst

O(n)

Space

O(k)

When to Use

Use Stratified Sampling when you need to partition a population into groups.
Use it for surveys with inputs like population.
Use it when randomization, representative samples, or controlled variation are needed.
Use it when the Sampling Design tradeoff is acceptable for the problem size.

When Not to Use

Avoid it when reproducibility, distribution quality, or sample independence cannot be verified.
Avoid it when the required output is not stratified sample.

What It Does

Partitions a population into groups
Samples within each group

Use Cases

Surveys
Monte Carlo integration
Balanced dataset sampling

Inputs

Population
Strata definitions
Sample allocation

Outputs

Stratified sample

Key Formulas (1)

Stratified estimate

estimate = ∑(weight_stratum · mean(sample_{values in stratum}))

estimate = sum(weight_stratum * mean(sample_values_in_stratum))

Combines separate group estimates according to each stratum's population weight.

Pseudocode

1.Assign each item to a stratum
2.Choose how many samples to draw per stratum
3.Randomly sample within each stratum
4.Combine stratum samples
5.Weight results if needed

Canonical Example

Input: items = [A, B, C, D], seed = 7
Output: sampled or randomized result
Explanation: Stratified Sampling: The algorithm uses controlled randomness to choose or generate values.

Implementation Notes

Keep the input contract explicit: Population; Strata definitions; Sample allocation.
Separate the random number source from the algorithm so tests can use fixed seeds.
Separate the random source from the sampler so tests can use fixed seeds and distribution checks.

Common Pitfalls

Good strata should group items that are similar for the quantity being estimated.
Sampling from the wrong distribution can make the estimate look precise but biased.
Using biased random choices or forgetting to store the seed for reproducible runs.
Handle empty, invalid, and boundary inputs before trusting stratified sample.

Interactive Mechanism Walkthrough

Iterative Convergence & State Trajectory

Show each population group contributing samples.

Step 1 of 5: Assign each item to a stratum

grouped-samples

Notes

Stratified Sampling operates in O(n) time and O(k) space within the Sampling Design family. Key governing relation: estimate = sum(weight_stratum * mean(sample_values_in_stratum)). Often compared with Latin Hypercube Sampling and Importance Sampling.