Who you ask decides what you find out. Everything else is arithmetic.
Spot the problem
A student wants to know how far the 1,200 learners in her school travel to get there. She asks the first 40 people who arrive at the gate in the morning. Why is her sample poor?
The method itself leans one way: arriving early is connected to living close by, so the sample is stacked with short journeys and her average will come out too low. That is bias. A is wrong — 40 out of 1,200 is a reasonable size; the trouble is who those 40 are, not how many. B would answer a different question, since the population is the learners.
Name both before collecting anything.
A census is the most accurate and usually impossible — nobody surveys all 1,200 learners for a class project. Sampling is the practical answer, and the whole skill is making the small circle resemble the big one.
| Primary | Secondary | |
|---|---|---|
| Where it comes from | your own survey, experiment or measurement | PSA reports, DepEd records, news articles, websites |
| Strength | exactly the question you wanted answered | large, cheap, already collected |
| Weakness | slow, and small | gathered for someone else's purpose, possibly out of date |
Counting the tricycles that pass your gate for an hour is primary. Quoting the PSA population count is secondary.
All four aim at the same thing: no group left out, no group over-represented.
| Method | How | In a school of 1,200 |
|---|---|---|
| Simple random | every person equally likely | draw 40 names from a hat with all 1,200 in it |
| Systematic | every k-th person on a list | 1,200 ÷ 40 = 30, so take every 30th name |
| Stratified | split into groups, sample each in proportion | take 8 from each grade level, since each has 240 |
| Cluster | pick whole groups at random | pick 2 sections at random and ask everyone in them |
Stratified is the one to reach for when the population splits into groups that might answer differently — grade levels, barangays, sections. It guarantees every group is heard in the right proportion.
A bigger biased sample is just a more confident wrong answer.
If the method excludes a group, asking more people excludes them more thoroughly. Only changing how you choose fixes bias.
Each group's share of the sample = its share of the population.
A high school has 300 Grade 7, 250 Grade 8, 200 Grade 9 and 250 Grade 10 learners. A stratified sample of 40 is wanted. How many come from each grade?
300 + 250 + 200 + 250 = 1,000
the whole population
40 ÷ 1,000 = 1 in every 25
the same fraction from every grade
300 ÷ 25 = 12, 250 ÷ 25 = 10, 200 ÷ 25 = 8
Grade 7: 12, Grades 8 and 10: 10 each, Grade 9: 8
12 + 10 + 8 + 10 = 40 ✓
the parts give back the sample size
Splitting 40 equally gives 10 per grade, which over-represents Grade 9 (200 learners) and under-represents Grade 7 (300 learners). Stratified means in proportion, so the bigger grade sends more.
The same question each time: who could be chosen, and who could not?
A town has 12 barangays. Survey A picks 3 barangays at random and asks every household in them. Survey B asks 5 random households from every barangay. Name each method.
A: whole groups, chosen at random
cluster sampling
B: some from every group
stratified sampling
Ask whether every group is represented: in B all 12 are, in A only 3.
The canteen puts out a suggestion box for a week and gets 150 slips, most of them complaints. Is this a fair picture of what learners think?
who answers? those who chose to
a volunteer (self-selected) sample
not fair: unhappy learners are likelier to write
biased toward strong opinions
When people pick themselves, the sample reflects who cared enough to respond, not the whole school.
A class adviser needs every learner's shirt size to order 38 class shirts. Sample or census?
population = 38 learners
small and easy to reach
census: ask all 38
every answer is needed, not an estimate
Sampling is for estimating a large population; when each individual's answer is used, ask everyone.
1,200 learners, sample of 40
what we want
k = 1,200 ÷ 40 = 30
population ÷ sample size
start at a random number 1–30
say 7
7, 37, 67, 97, …
every 30th name after that
The random start matters. Always beginning at 1 would make the method predictable, and a list ordered by something meaningful could then tilt the sample.
Data-collection items describe a survey and ask you to name the method, spot why it is biased, or compute an interval or a stratified share. The fastest route is to ask how each person was chosen and who could never have been; the 10-second check for a calculation is that the shares add back to the sample size.
Name the method
A barangay has 400 households in Zone 1, 600 in Zone 2 and 200 in Zone 3. A health worker surveys 20 households from Zone 1, 30 from Zone 2 and 10 from Zone 3. Which sampling method is this?
The population was split into zones and each zone was sampled in proportion — 20 of 400, 30 of 600, 10 of 200 is 5% every time. That is stratified sampling. Cluster would have meant picking whole zones and surveying everyone in them, and systematic would have meant every k-th household on one list.
Hint: work out what fraction of each zone was surveyed. If it is the same fraction every time, the groups were deliberately kept in proportion.
