Ask a few, guess for all

The idea

A probability estimated from data collected from a sample is applied to the whole population; a larger and more representative sample gives a more confident estimate. This process is called sampling.

Too many to ask

A school of 1500 students needs fruit for everyone. You want to know how many students like mango. Asking all 1500 takes too long.

What is a sensible way to find out?

• Ask a smaller group and use their answers
• Ask nobody and just guess
• Ask only one friend

Take samples

Ask samples of different sizes. Try samples of 10 and 100 from the whole school, then a sample from one class only. Compare the estimates.

Use a sample

A probability estimated from a sample is applied to the whole population. A larger and more representative sample gives a more confident estimate. This is sampling.

If 20 of 50 students like mango, the estimate is 20/50 = 0.4. For a school of 1500: 0.4 × 1500 = 600 mangoes.

Notes

Sampling: estimate a probability from a sample, then apply it to the population. A larger, more representative sample gives a more confident estimate.

Check yourself

In a sample of 50 students, 20 like mango. About how many of the 1500 students would you expect to like mango?

Answer: 600

0.4 × 1500 = 600 students.

Which sample gives the most confident estimate for the whole school?

The population in this school example is…

A sample of 100 students shows a probability of 0.3 for apples. About how many of the 1500 students like apples?

Answer: 450

0.3 × 1500 = 450 students.

• 100 students from many classes and grades — correct. Yes. It is larger and covers different kinds of students.
• 10 students from one class. It is small and comes from one class only.
• Your 3 best friends. It is tiny and not representative of the school.
• The 50 students we asked. They are the sample.
• All 1500 students of the school — correct. Yes. The population is everyone we want to know about.
• The students who like mango. They are only part of the population.