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NotesMath AA SLTopic 4.1Sampling techniques
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4.1.22 min read

Sampling techniques

IB Mathematics: Analysis and Approaches • Unit 4

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Contents

  • The five sampling techniques
  • Random & systematic
  • Stratified sampling (the calculation)
  • Quota, convenience & spotting bias
Five named ways to pick a sample: The IB syllabus names five ways to choose a sample. A common exam question gives you a scenario and asks you to name the technique used.
The five techniques: • Simple random — every member equally likely (draw lots / random numbers). • Systematic — order the list, take every k-th member. • Stratified — split into groups, sample each in proportion. • Quota — fill fixed numbers per group, chosen non-randomly. • Convenience — whoever is easiest or first available.

IB-style question — name the technique

A manager puts all 200 staff names in a hat and draws out 20 for a survey. Which sampling technique is this?

Step by step

  1. Every staff member is equally likely to be drawn, purely by chance.
  2. That is the definition of one technique.

Final answer

Simple random sampling.

Equal chance, or every k-th: Simple random: every member has an equal chance (random numbers / drawing lots). Systematic: order the list and take every k-th member after a random start, where k = population size ÷ sample size.

IB-style question — systematic interval

A club has 800 members. A sample of 50 is taken systematically. Find the sampling interval and describe how to choose the sample.

Step by step

  1. Interval = population ÷ sample size.
  2. Pick a random start, then step by k.

Final answer

k = 16: choose a random starting member from the first 16, then take every 16th member after that.

Random start matters: Systematic sampling needs a random first member — otherwise you always pick the same positions and could introduce bias.

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Sample each group in proportion to its size: Stratified sampling splits the population into groups (strata) and takes from each group a number proportional to its size — so big groups contribute more.
Stratified allocation — the proportion of the group, times the total sample size.

IB-style question — how many from a group

A school has 600 junior and 400 senior students (1000 in total). A stratified sample of 50 is taken. Find how many juniors should be in the sample.

Step by step

  1. Write the group's proportion times the sample size.
  2. Evaluate.

Final answer

30 juniors (and so 20 seniors).

Check it adds up: The numbers from all strata should sum to the total sample size (here 30 + 20 = 50).
Non-random methods risk bias: Quota fills fixed numbers from each group but picks members non-randomly; convenience takes whoever is easiest/first. Because selection isn't random, these are the most likely to be biased.

Random-based (fairer)

  • simple random — equal chance
  • systematic — every k-th
  • stratified — proportional groups

Non-random (bias risk)

  • quota — fixed numbers, chosen non-randomly
  • convenience — easiest / first available
  • often unrepresentative

IB-style question — name it and judge it

A reporter interviews the first 30 people leaving a train station at 9 am. Name the sampling technique and give one reason the sample may be biased.

Step by step

  1. First / easiest available → name the technique.
  2. Who is missing?

Final answer

Convenience sampling; biased because only people travelling at 9 am are included, so it doesn't represent everyone.

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A library has 1200 members. A sample of 60 is chosen using computer-generated random numbers. Name the sampling technique used. [1 mark]

Related Math AA SL Topics

Continue learning with these related topics from the same unit:

4.1.1Populations & samples
4.2.1Frequency & histograms
4.2.2Cumulative frequency
4.2.3Box plots
View all Math AA SL topics

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