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 CaSQ 20 - Taking a Stratified Sample from a Data Set
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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 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.
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This page last updated 12 February 2013 | 
