GCSE Maths · Higher · Chapter 18: Sampling and more complex diagrams · Lesson 1

Sampling

Grades 4–7About 45 minutesCalculator allowed35 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Work out $\frac{1}{9}$ of $360$ .
[1 mark]
Answer
A2
From chapter 8
Make $x$ the subject of $y = \frac{x - 3}{3}$ .
[1 mark]
Answer
A3
From chapter 3
45 people were asked. 8 said yes. Find the angle for "yes" on a pie chart.
[1 mark]
Answer
A4
From chapter 14
Work out $(4 \times 1 0^{3}) \times (3 \times 1 0^{3})$ . Give your answer in standard form.
[1 mark]
Answer

Grades 4–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

A club of $960$ has $384$ adults, $336$ students and $240$ seniors. How many of each go in a stratified sample of $40$ ?

Hint Find the fraction sampled, then take that fraction of each group.

B1
A gym of $750$ has $300$ bronze, $270$ silver and $180$ gold members. How many of each go in a stratified sample of $50$ ?
[3 marks]
Answerbronze $\dots$ silver $\dots$ gold $\dots$

Example 2

A stratified sample of $48$ from a club includes $6$ of its $90$ juniors. How many members does the club have?

Hint The fraction of juniors sampled is the fraction of the club sampled.

B2
A stratified sample of $35$ from a hospital includes $8$ of its $112$ part-time staff. How many staff does the hospital have?
[3 marks]
Answer

Grades 5–6

C1
A council asks $200$ drivers in a car park whether the town needs more buses. Give one reason the sample may be biased.
[1 mark]
C2
A school of $1350$ takes a random sample of $54$ . Find the probability that a given student is chosen, in its simplest form.
[2 marks]
Answer

C3
A factory has $1200$ workers and $228$ work nights. How many night workers are in a stratified sample of $75$ ?
[2 marks]
Answer
C4
Students are numbered $001$ to $650$ . These random numbers are read: $427$ , $083$ , $711$ , $427$ , $650$ , $000$ . Which students are picked?
[2 marks]
Answer
C5
A head teacher wants to know what the school's $1200$ students think of a new timetable. Give one advantage and one disadvantage of asking a sample of students instead of all $1200$ .
[2 marks]
C6
A college has $900$ students. Describe how the college could take a random sample of $45$ students.
[2 marks]

Grades 6–7

D1
A club has $120$ juniors and $360$ adults. Leah asks $20$ juniors and $20$ adults. She says, "My sample of $40$ is stratified because it has both groups."
Explain why Leah is wrong, and work out a stratified sample of $40$ .
[3 marks]

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out how many of each group go in a stratified sample.
I can work back from a sample to the size of the population.
I can say why a sample may be biased.

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