Step 1: the barangay's proportional allotment
In proportional allocation, each barangay's share of the sample matches its share of the population. The municipality has 4,800 listed households and the total sample is 400. For a barangay with 600 households, the allotment is 400 × 600 ÷ 4,800 = 50 households. This barangay holds one-eighth of all households, so it receives one-eighth of the sample.
Step 2: the sampling interval
Systematic sampling picks units at a fixed interval from an ordered list. The sampling interval (k) is the number of units in the list divided by the number to be sampled: k = 600 ÷ 50 = 12. The nurse picks a random start from 1 to 12, then takes every 12th household on the list after it. For example, with a random start of 7, she selects households 7, 19, 31, and so on. Check: 600 ÷ 12 = 50 households, exactly the allotment.
| Step | Formula | Result |
|---|
| Allotment | 400 × 600 ÷ 4,800 | 50 households |
| Interval (k) | 600 ÷ 50 | 12 |
| Random start | Random number from 1 to k | From 1 to 12 |
| Check | 600 ÷ 12 | 50 households |
How each distractor was built
An interval of 50 uses the allotment itself as the interval; every 50th household would give only 12 households. An interval of 27 comes from giving every barangay an equal share (400 ÷ 18 ≈ 22, then 600 ÷ 22 ≈ 27), which ignores the proportional allotment. An interval of 8 divides the municipal total by the barangay total (4,800 ÷ 600); every 8th household would give 75 households, too many. Watch out! The interval is always list size divided by sample size for that list, and the allotment must be found first.
Exam takeaway
Find the allotment first, then divide the list size by the allotment to get k, and pick the random start between 1 and k. Systematic sampling is easy to carry out in the field with a household list, but the nurse should check that the list has no repeating pattern every 12 households, such as a corner house at regular intervals, which could bias the sample.