Simple random sampling
Simple random sampling.
- Start with a complete list. Give every member a unique number.
- Select distinct numbers at random, without replacement, until the sample is complete.
- Each possible sample of the chosen size should have the same chance. Random does not mean guaranteed representative.
Example 1
A club has 60 members. Describe how to select a simple random sample of 6 different members.
Use the complete membership list. Every possible set of 6 members should have the same chance.
Example 2
Members are numbered 1–30. A random digit table gives 08, 08, 34, 12, 27, 03. Select 4 different members.
Ignore the repeated 08 and the out-of-range 34; continue until 4 distinct valid numbers are selected.
Your turn
A librarian wants a simple random sample of 5 books from 200. Describe a method.
Check answer
Do not restrict the selection to one shelf.
A teacher selects the first 8 names on an alphabetical class list. Is this a simple random sample?
Check answer
The same first 8 students are always selected; other sets of 8 have no chance.
Twenty identical folded slips each contain a different student’s name. Describe how to sample 4 students at random.
Check answer
Identical slips and random mixing avoid favouring particular students; no replacement prevents repeats.
A random generator selects 14, 06, 14, 29 and 11 from a list of 30. A sample of 4 different students is needed. What should be kept?
Check answer
Discard the repeated 14. Repeated draws do not count as additional people in the sample.
A school randomly chooses 20 students from a complete list. Must the sample contain the same proportion from each year as the school?
Check answer
Random selection gives an unbiased selection procedure; it does not guarantee exact group proportions in the resulting sample.
A librarian wants a simple random sample of 5 books from 200. Describe a method.
AnswerDo not restrict the selection to one shelf.
A teacher selects the first 8 names on an alphabetical class list. Is this a simple random sample?
AnswerThe same first 8 students are always selected; other sets of 8 have no chance.
Twenty identical folded slips each contain a different student’s name. Describe how to sample 4 students at random.
AnswerIdentical slips and random mixing avoid favouring particular students; no replacement prevents repeats.
A random generator selects 14, 06, 14, 29 and 11 from a list of 30. A sample of 4 different students is needed. What should be kept?
AnswerDiscard the repeated 14. Repeated draws do not count as additional people in the sample.
A school randomly chooses 20 students from a complete list. Must the sample contain the same proportion from each year as the school?
AnswerRandom selection gives an unbiased selection procedure; it does not guarantee exact group proportions in the resulting sample.