AI generatedStatisticsGCSE Higher / IGCSE Extended

Stratified sampling calculations

Stratified sampling calculations.

Named sampling methods vary by course. Check your specification or teacher’s guidance.

  • Split the population into non-overlapping groups that together cover everyone.
  • Sample from a group = group population ÷ total population × sample size.
  • Choose randomly within each group. If rounding is needed, keep sensible proportions and check the allocations still total the required sample.

Example 1

Select a proportional stratified sample of 40. Find the number to choose from each group.

Given information
GroupPopulation
A40
B60
C100
Keep the same proportions in the sample
GroupPopulationSample
A408
B6012
C10020
Total20040

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 40.

Example 2

Select a proportional stratified sample of 22. Find the number to choose from each group.

Given information
GroupPopulation
A50
B60
C110
Keep the same proportions in the sample
GroupPopulationSample
A505
B606
C11011
Total22022

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 22.

Your turn

Question 1

Select a proportional stratified sample of 48. Find the number to choose from each group.

Given information
GroupPopulation
A60
B60
C120
Check answer
Keep the same proportions in the sample
GroupPopulationSample
A6012
B6012
C12024
Total24048

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 48.
Question 2

Select a proportional stratified sample of 26. Find the number to choose from each group.

Given information
GroupPopulation
A70
B60
C130
Check answer
Keep the same proportions in the sample
GroupPopulationSample
A707
B606
C13013
Total26026

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 26.
Question 3

Select a proportional stratified sample of 48. Find the number to choose from each group.

Given information
GroupPopulation
A80
B60
C100
Check answer
Keep the same proportions in the sample
GroupPopulationSample
A8016
B6012
C10020
Total24048

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 48.
Question 4

Select a proportional stratified sample of 26. Find the number to choose from each group.

Given information
GroupPopulation
A90
B60
C110
Check answer
Keep the same proportions in the sample
GroupPopulationSample
A909
B606
C11011
Total26026

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 26.
Question 5

Select a proportional stratified sample of 56. Find the number to choose from each group.

Given information
GroupPopulation
A100
B60
C120
Check answer
Keep the same proportions in the sample
GroupPopulationSample
A10020
B6012
C12024
Total28056

Black: given data. Blue: working we add.

Total populationThe groups must cover the population without overlap.
Group A sampleGroup population ÷ total population × total sample. Repeat for each group.
Randomly choose the calculated number within each group. Check the allocations add to 56.
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