Education Services home page > CensusAtSchool home page > Year 8 Resources
CaSQ 20  Taking a Stratified Sample from a Data Set
You can download this activity and the solution as a rich text file (RTF) using the link at the bottom of the page.
Task:
A stratified random sample is used when distinct groups or strata are identified as important within a data set. By using this sampling method, each group is represented in the sample in the same proportion as in the population from which the sample is drawn.
For example if I decide to collect a sample of 20 from a population of 600 boys and 400 girls then each group in the sample will be represented in the same fraction by:
Boys 600/1000 = 60% and girls 400/1000 = 40%. Therefore, in the sample of 20 you would need to randomly select 60% of 20 = 12 boys, and 40% of 20 = 8 girls.
Look at the following data showing the number of students who filled in a questionnaire in the 2008 CensusAtSchool project.
Year Level  ACT  NSW  NT  QLD  SA  TAS  VIC  WA  Year Totals 
Year 4 or below  12  919  5  77  176  152  549  176  2066s 
Year 5  171  2321  19  208  350  419  2070  587  6145 
Year 6  176  3235  29  452  782  654  2674  590  8592 
Year 7  57  1379  25  801  1007  376  1411  1272  6328 
Year 8  76  2131  17  860  1329  536  1095  954  6998 
Year 9  33  1857  18  1016  1244  518  950  912  6548 
Year 10  30  1100  17  677  1054  354  502  914  4648 
Year 11  49  447  41  343  536  194  205  159  1974 
Year 12  27  105  3  227  253  38  49  78  780 
Other  7  20  4  10  14  8  29  18  110 
Total  638  13514  178  4671  6745  3249  9534  5660  44,189 
Table 1: Number of students who completed the CensusAtSchool questionnaire by year level and State
1. Name two ways that this data has been organised that could be used to make stratified random samples.
2. A total of 44,189 students participated in the 2008 CensusAtSchool questionnaire. For a stratified sample based on the State for each student, calculate the numbers in the sample for each State if the sample size is to be 100.
a) Give your answers accurate to 2 decimal places.
b) Round this number to the nearest whole number.
c) Check that you total for the whole number calculations add up to 100.
Year
Level  ACT  NSW  NT  QLD  SA  TAS  VIC  WA  Year
Totals 
total  638  13514  178  4671  6745  3249  9534  5660  44189 
2 dp          
nearest whole number          
Table 2: Number of students who completed the CensusAtSchool questionnaire by State
3. For a sample size of 50 calculate the number needed if you formed stratified sample according to the Year Level of each student.
a) Give your answers accurate to 2 decimal places.
b) Round this number to the nearest whole number.
c) Check that your total for the whole number calculations add up to 50.
Table 3: Number of students who completed the CensusAtSchool questionnaire by Year Level
Extension:
For each of the following, based on a coeducational school population of 1000 students, decide whether or not you think that it would be warranted to obtain a stratified random sample rather than a simple random sample. If so, what strata would you include and why?
1. The junior school coordinator wants to know if junior students want the lunchtime equipment program to continue.
2. The canteen wants to sample students to see whether students like the food on their current menu.
3. The Principal wants students’ opinion on whether to include a blazer in the uniform.
4. The Sport teachers want to know whether to include aerobics, soccer or surfing on their elective program.
5. The library isn’t sure whether to continue its subscription to “Girlfriend” magazine.
Download the full activity: 

Download the solution: 


This page last updated 12 November 2013 