Population and sample: why we survey only some

0:00A school of 900 students wants to know their favourite lunch. Each dot is one student.

0:07The population is the whole group we want to learn about: here, all 900 students.

0:14Asking every member of the population is called a census. For 900 students, that takes too long.

0:22So the school asks a sample instead: a smaller group of 90 students taken from the population.

0:29The 90 are picked at random, so every student has the same chance of being chosen.

0:3536 of the 90 choose pasta, and the other 54 choose something else.

0:4136 out of 90 is 36 divided by 90, which is 0.4, or 40 percent.

0:49Check: one row of 9 is 10 percent of 90, and 4 times 9 is 36.

0:56Now we estimate, which means make a careful guess, for all 900. 40 percent of 900 is 0.4 times 900, which is 360.

1:11Check: 900 is 10 times 90, so the estimate is 10 times 36, which is 360.

1:21So about 360 of the 900 students would choose pasta. It is an estimate, not an exact count.

1:29A common mistake is to trust a big sample even when it was chosen unfairly.

1:35Suppose we ask 300 students lining up at the pasta counter.

1:40That sample is biased: it was chosen in a way that favours pasta fans.

1:45A smaller random sample, like our 90, usually gives a better estimate than a big biased one.

1:53In short: survey a fair, random sample, then scale its result up to estimate the population.