Sampling methods: simple random, stratified, cluster, systematic

About this lesson

Statistics (AP-aligned) › Collecting data

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Sampling methods: simple random, stratified, cluster, systematic

Warm-up

Three quick questions from earlier lessons.

Discover

A school has 600 juniors and 400 seniors. You want a sample of 50 that reflects both grades. How many juniors?

  1. 30
  2. 25

Key idea

Random sampling methods.

Simple random sample (SRS): every group of nn individuals is equally likely. Stratified: split into similar groups (strata) and take an SRS from each. Cluster: split into groups (clusters), choose some clusters at random, take everyone in them. Systematic: a random start, then every kkth individual.

Worked example

A list of 2,400 members; a systematic sample of 80.

Step k=30k = 30
2,400 ÷ 80.
Start at, say, member 17
Random start among the first 30.
17, 47, 77, … up to 80 members
Then add 30 each time.

Your turn, guided

Your turn: 900 members, systematic sample of 45. The step.

k=20k = 20
900 ÷ 45.

Practice ★

  1. A school has 600 juniors and 300 seniors. A stratified sample of 90 students is taken in proportion to grade. How many juniors are in the sample?
  2. A school has 500 juniors and 600 seniors. A stratified sample of 110 students is taken in proportion to grade. How many juniors are in the sample?
  1. A systematic sample of 30 customers is taken from a list of 480: a random start, then every kkth name. What is kk?

Watch out!

Practice ★★

  1. A district has 60 classrooms. Five are chosen at random and every student in them is surveyed. Which sampling method is this?
    1. Cluster sampling
    2. Stratified sampling
    3. A simple random sample of students
  1. Boss problem. A town has 300 houses in the north and 600 in the south. A stratified sample of 180 houses is planned, in proportion to each area.

Exit ticket

Three questions to check you have got it.

  1. A school has 600 juniors and 300 seniors. A stratified sample of 90 students is taken in proportion to grade. How many juniors are in the sample?
  2. A school has 500 juniors and 600 seniors. A stratified sample of 110 students is taken in proportion to grade. How many juniors are in the sample?
  3. A school has 900 juniors and 800 seniors. A stratified sample of 170 students is taken in proportion to grade. How many juniors are in the sample?

Summary card

Sampling methods

SRS · stratified (some from every group) · cluster (all from some groups) · systematic (every kkth).

Watch out: proportional allocation in stratified samples.

End of the lesson

Next lesson: Bias in sampling Back to the chapter

Answers: Sampling methods: simple random, stratified, cluster, systematic

A

  1. 6060
  2. 5050

B

  1. 1616

C

  1. Cluster sampling

D

  1. 120120

E

  1. 6060
  2. 5050
  3. 9090

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