# Australian Bureau of Statistics

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 CensusAtSchool Australia

CaSQ 20 - Taking a Stratified Sample from a Data Set

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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.

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.
b) Round this number to the nearest whole number.
c) Check that your total for the whole number calculations add up to 50.
 Year Level year totals 2 dp nearest whole number Year 4 or below 2066 Year 5 6145 Year 6 8592 Year 7 6328 Year 8 6998 Year 9 6548 Year 10 4648 Year 11 1974 Year 12 780 Other 110 Total 44189
Table 3: Number of students who completed the CensusAtSchool questionnaire by Year Level

Extension:

For each of the following, based on a co-educational 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.