Practise 18 exam-style questions on Sampling and populations for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.
18 questions
1–5 marks each
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18 questions, marked as you go
Sample questions with model answers
Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.
Question 1
2 marks
Jo asks a random sample of 40 students at her school how they travel to school. 14 of the students in the sample walk to school. There are 900 students at the school.
Work out an estimate for the number of students at the school who walk to school.
Model answer
Proportion who walk in the sample \(= \dfrac{14}{40} = 0.35\) Estimate \(= 0.35 \times 900 = 315\)
Explanation
A random sample should be representative of the population, so assume the same proportion of the whole school walks as in the sample. Find the fraction who walk in the sample and multiply it by the population size.
Mark scheme
1 mark
M1 for \(\dfrac{14}{40} \times 900\) oe
e.g. 900 ÷ 40 × 14, or 0.35 × 900; correct answer with no working scores full marks
1 mark
A1 for 315
cao
Question 2
2 marks
Leah asked a random sample of commuters in a city how they travel to work. The pie chart shows her results. There are 1800 commuters in the city.
Work out an estimate for the number of commuters in the city who travel to work by train.
Model answer
Fraction who travel by train \(= \dfrac{100}{360} = \dfrac{5}{18}\) Estimate \(= \dfrac{5}{18} \times 1800 = 500\)
Explanation
The angle of a sector out of 360° gives the fraction of the sample in that category. Assuming the sample represents the city, apply the same fraction to all 1800 commuters. You do not need to know how many people were in the sample.
Mark scheme
1 mark
M1 for \(\dfrac{100}{360} \times 1800\) oe
e.g. 1800 ÷ 360 × 100; correct answer with no working scores full marks
1 mark
A1 for 500
cao
Question 3
3 marks
A farmer collects 600 eggs. She weighs a random sample of 20 of these eggs. The total mass of the 20 eggs is 1240 g.
Work out an estimate for the total mass of all 600 eggs. Give your answer in kilograms.
Model answer
Mean mass of an egg in the sample \(= 1240 \div 20 = 62\) g Estimated total mass \(= 62 \times 600 = 37\,200\) g \(37\,200 \text{ g} = 37.2 \text{ kg}\)
Explanation
Use the sample mean as an estimate of the mean mass of all the eggs, then multiply by the number of eggs. Equivalently, 600 eggs is 30 times the sample, so multiply 1240 g by 30. Divide by 1000 to change grams to kilograms.
Mark scheme
1 mark
M1 for 1240 ÷ 20 (= 62) or 600 ÷ 20 (= 30)
correct answer with no working scores full marks
1 mark
M1 for 62 × 600 or 1240 × 30 (= 37 200)
1 mark
A1 for 37.2 kg
37 200 g with no conversion scores M1 M1 A0
Question 4
4 marks
There are 1200 students at a college. Amy takes a random sample of 60 of these students. 24 of the students in her sample have a part-time job. The mean weekly earnings of these 24 students is £35.
Work out an estimate for the total weekly earnings of all the students at the college who have a part-time job. Give one reason why your estimate might not be accurate.
Model answer
Estimated number with a job \(= \dfrac{24}{60} \times 1200 = 480\) Estimated total weekly earnings \(= 480 \times £35 = £16\,800\) The estimate might not be accurate because it is based on only 60 students, who may not be representative of the whole college.
Explanation
First use the sample proportion to estimate how many students at the college have a job, then use the sample mean to estimate their total earnings. Every estimate made from a sample has a limitation: a different random sample would usually give a different answer.
Mark scheme
1 mark
P1 for \(\dfrac{24}{60} \times 1200\) (= 480)
oe; correct answer with no working scores full marks
1 mark
P1 for 480 × 35
ft their 480
1 mark
A1 for £16 800
cao
1 mark
C1 for a correct reason, e.g. the sample of 60 may not be representative of all 1200 students
accept: earnings may vary from week to week; students may not give accurate answers; a different sample would give a different result
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