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Statistics

Sampling Methods

Lesson

How you pick a sample shapes what you can conclude. The five common methods, from best to worst for unbiased inference:

1. Simple random sample (SRS)

Every member of the population has an equal chance of being selected. Names from a hat, or a random-number generator across all IDs.

2. Stratified sample

Split the population into strata (groups that share a key trait — grade, region, age band), then take a random sample from each stratum. Good for making sure each subgroup is represented.

3. Systematic sample

Pick every kkth person on a list (e.g. every 10th customer). Cheap and easy, but can be biased if the list has hidden periodicity.

4. Cluster sample

Split the population into clusters (e.g. schools, zip codes), randomly pick a few clusters, then sample every member of those clusters. Easier to administer but less precise than SRS.

5. Convenience sample

Just sample whoever is easy to reach. Quick, but highly biased — rarely reflects the population.

How to type your answer

Type the number for the sampling method: 1 random, 2 stratified, 3 systematic, 4 cluster, 5 convenience.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Names are drawn from a hat. Sampling method?\text{Names are drawn from a hat. Sampling method?}

Problem 2

Every 10th person leaving a store is surveyed. Method?\text{Every 10th person leaving a store is surveyed. Method?}

Problem 3

Survey only friends you can reach easily. Method?\text{Survey only friends you can reach easily. Method?}

Problem 4

Sample from each grade level. Method?

Practice

Standard problems matching the lesson.

Problem 5

Pick 50 random student IDs from a full enrollment list.\text{Pick 50 random student IDs from a full enrollment list.}

Problem 6

5 random schools, all students. Method?

Problem 7

Survey every 5th house on a street.\text{Survey every 5th house on a street.}

Problem 8

Random from each worker group. Method?

Problem 9

Stand at the mall entrance and ask whoever walks by.\text{Stand at the mall entrance and ask whoever walks by.}

Problem 10

Randomly select 100 employees from the full company list.\text{Randomly select 100 employees from the full company list.}

Problem 11

Pick a region, survey all there. Method?

Problem 12

Random from each region. Method?

Problem 13

Use the first 30 students who reply to your email.\text{Use the first 30 students who reply to your email.}

Problem 14

Generate 20 random phone numbers and call them.\text{Generate 20 random phone numbers and call them.}

Problem 15

Survey every 100th name in the phone book.\text{Survey every 100th name in the phone book.}

Problem 16

Divide voters by age group, sample proportionally from each.\text{Divide voters by age group, sample proportionally from each.}

Problem 17

A pollster knocks at every 5th door on a block.\text{A pollster knocks at every 5th door on a block.}

Problem 18

A teacher surveys only students who stayed after class.\text{A teacher surveys only students who stayed after class.}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

3 random ZIPs, all households. Method?

Problem 20

A factory inspects every 50th product on the assembly line.\text{A factory inspects every 50th product on the assembly line.}

Problem 21

100 per climate zone. Method?

Problem 22

RNG from voter list. Method?

Problem 23

Online form respondents. Method?

Problem 24

5 ZIPs, everyone in them. Method?

Problem 25

A coach surveys players in the first 3 rows of bleachers.\text{A coach surveys players in the first 3 rows of bleachers.}

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Quiz

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