A population is the whole group you want to know about; a sample is the part you ask. A random sample gives everyone an equal chance of being chosen, so it is less likely to be biased.
Say who the population is.
Check how the sample was chosen and whether some people could not be picked.
A bigger random sample gives a more reliable result.
Watch out Asking only people in one place or at one time can bias the sample.
See it worked
Worked exampleNon-calculator·2 marks
A head teacher wants to know how long the 900 students at her school spend on homework each week.
(a) Which sample is most likely to represent the whole school?
(b) Explain why the homework club sample would be biased.
(a) A random sample from the whole population gives every student the same chance of being chosen.
(b) The sample is not typical: the reason they are in it is linked to what is being measured.
Answer (a) 50 students picked at random from the whole school register; (b) Students at homework club are likely to spend more time on homework than other students.
Your turn
Question 1Calculator allowed·2 marks
A college has 850 students. In a random sample of 50 students, 14 usually cycle to college.
Use this sample to estimate how many of the 850 students usually cycle to college.
Question 2Calculator allowed·3 marks
A council investigates heat pumps on two housing estates.
Estate A has 360 homes. A representative sample of 60 homes includes 17 with heat pumps.
Estate B has 540 homes. A representative sample of 90 homes includes 22 with heat pumps.
Estimate the total number of homes with heat pumps on the two estates.
Question 3Non-calculator·3 marks
A council has 360 residents. It surveys 30 people leaving a cycling shop; 10 cycle daily.
(a) Calculate the population estimate obtained by scaling this sample.
(b) Explain why the council should not trust this as a representative estimate.
Write your answer, then show the working
(a) Scale the observed sample fraction to the population. 10/30×360
Therefore 120.
(b) Cycling-shop customers are likely to cycle more often than the whole population. The selection method is biased.
Answer (a) 120; (b) Cycling-shop customers are likely to cycle more often than the whole population. The selection method is biased.
In past papers
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