📊 Data
📋Surveys & Sampling
What to ask, whom to ask, how many to ask — every fork in survey design hides a trap.
The canteen wants to add a new dish, but there's no way to ask all 1200 students — so ask 60. Whom? How many? How? Fumble any step and the numbers that come back will lie. Survey design is half mathematics, half detective work.
Ask the question right first
The question itself can set the rhythm:
- Presuming the answer: "How much do you like the new dish?" — before anyone speaks, liking is assumed;
- Incomplete options: "Like / Really like" — those who dislike it are forced to pick anyway;
- Revised: "What's your take on the new dish?" with options: really like / it's okay / dislike — every attitude gets a door.
The standard for a good question: no answer presumed, options covering every possibility, wording kept neutral.
Population and sample
- Population: everyone you want to know about — all 1200 students;
- Sample: the part you actually ask — the 60 interviewed.
The whole point of a survey is to guess the population from the sample: the tastes of 60 must stand in for the tastes of 1200. Whether the sample deserves that trust depends on the next step — how people are picked.
Why random
The laziest approach is to grab whoever is nearby: your classmates at break, or a lap of the basketball club. That's a convenience sample, and it has a fatal flaw — classmates share tastes, basketball players all love sports drinks, and what you collect is a small-circle opinion, not the school's.
Random sampling gives every person an equal chance of being picked, like flipping a coin (the math behind it lives in Probability for Beginners): heads or tails, nobody gets to decide. Only then can small-circle preferences fail to bend the result.
Two crash sites
"What sport does the whole school love?" — survey handed out only in the basketball club, and the answer leans all the way to basketball. "When is the canteen most crowded?" — counted only at noon, so every other time slot is assumed away. The shared root: a sample that never covered the population, yet claimed to speak for it.
Random Sampling
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Heads rate
The more you flip, the closer the heads rate gets to 50% — that's the law of large numbers.
Pretend each coin flip is "pick one person at random". In 10 flips, 8 heads is nothing strange — small samples run on luck; over thousands of flips, the ratio settles close to even. Sampling works the same: the bigger the sample, the steadier the result, and the more confidently it can speak for the population.
Serving the results
Once asked, the numbers must be readable at a glance: tally each option and draw a Bar Graphs chart, and who leads and by how much stands out instantly. And always state three things — whose sample it was, how many, and how they were picked. Numbers with no head or tail are as good as made up.
Check yourself
Quick quiz
1. What's wrong with the question “How much do you like the new uniform”?
2. You want the opinion of all 1000 students but only ask your 5 best friends. What is the biggest problem?
3. In 10 coin flips you get 8 heads. Can you conclude the coin is unfair?