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Sampling & bias practice questions with answers

Foundation and Higher · Grade 4

A second set of sampling & bias questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

In a fair random sample of 40 students, 18 say they like the new menu. The school has 440 students. Estimate how many students in the school like the new menu.

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Answer: 198

  1. The fraction of the sample who like the menu is 18/40.
  2. Use the same fraction for the whole school: 18/40 × 440.
  • Method (1): The fraction of the sample who like the menu is 18/40.
  • Accuracy (1): Answer 198

Question 2 Easy

In a random sample of 5 people, 2 own a bike. What percentage of the sample own a bike?

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Answer: 40

  1. Fraction who own a bike = 2/5.
  2. 2 ÷ 5 = 0.4.
  • Method (1): Fraction who own a bike = 2/5.
  • Accuracy (1): Answer 40

Question 3 Medium

In a random sample of 8 people, 2 own a bike. What percentage of the sample own a bike?

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Answer: 25

  1. Fraction who own a bike = 2/8.
  2. 2 ÷ 8 = 0.25.
  • Method (1): Fraction who own a bike = 2/8.
  • Accuracy (1): Answer 25

Question 4 Medium

A school has 600 students. A random sample of 30 students is taken. What percentage of the students are in the sample?

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Answer: 5

  1. Fraction in the sample = 30/600.
  2. 30 ÷ 600 = 0.05.
  • Method (1): Fraction in the sample = 30/600.
  • Accuracy (1): Answer 5

Question 5 Hard

A school has 200 students. A random sample of 16 students is taken. What percentage of the students are in the sample?

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Answer: 8

  1. Fraction in the sample = 16/200.
  2. 16 ÷ 200 = 0.08.
  • Method (1): Fraction in the sample = 16/200.
  • Accuracy (1): Answer 8

Question 6 Hard

In a fair random sample of 40 students, 11 say they like the new menu. The school has 560 students. Estimate how many students in the school like the new menu.

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Answer: 154

  1. The fraction of the sample who like the menu is 11/40.
  2. Use the same fraction for the whole school: 11/40 × 560.
  • Method (1): The fraction of the sample who like the menu is 11/40.
  • Accuracy (1): Answer 154

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

In a random sample of 20 people, 9 own a bike. What percentage of the sample own a bike?

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Answer: 45

  1. Fraction who own a bike = 9/20.
  2. 9 ÷ 20 = 0.45.
  3. 0.45 × 100 = 45%.
  • Method (1): Fraction who own a bike = 9/20.
  • Accuracy (1): Answer 45

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

In a fair random sample of 40 students, 12 say they like the new menu. The school has 440 students. Estimate how many students in the school like the new menu.

  1. 132
  2. 5280
  3. 308
Show answer

132 The result is 132.

Check 2

In a random sample of 20 people, 9 own a bike. What percentage of the sample own a bike?

  1. 45
  2. 9
  3. 0.45
Show answer

45 The result is 45.

Check 3

A school has 1000 students. A random sample of 150 students is taken. What percentage of the students are in the sample?

  1. 15
  2. 150
  3. 0.15
Show answer

15 The result is 15.

Check 4

A council wants the views of the 5000 adults in a town. Which method is best? A: Ask people leaving a gym on Monday morning. B: Ask people who reply to a social media post. C: Pick names at random from a list of all the adults in the town.

  1. C
  2. A
  3. B
Show answer

C The result is C.

Check 5

In a random sample of 4 people, 3 own a bike. What percentage of the sample own a bike?

  1. 75
  2. 3
  3. 0.75
Show answer

75 The result is 75.

Check 6

A school has 250 students. A random sample of 20 students is taken. What percentage of the students are in the sample?

  1. 8
  2. 20
  3. 0.08
Show answer

8 The result is 8.

Check 7

In a fair random sample of 40 students, 13 say they like the new menu. The school has 320 students. Estimate how many students in the school like the new menu.

  1. 104
  2. 4160
  3. 216
Show answer

104 The result is 104.

Check 8

A shop wants a random sample of 20 of its 240 customers who have a loyalty card. Which method is best? A: Give each card number a place in a list and pick 20 using random numbers. B: Ask the first 20 customers on Saturday. C: Ask 20 customers who are buying the most expensive items.

  1. A
  2. B
  3. C
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A The result is A.

Check 9

A school has 400 students. A random sample of 60 students is taken. What percentage of the students are in the sample?

  1. 15
  2. 60
  3. 0.15
Show answer

15 The result is 15.

Check 10

In a fair random sample of 40 students, 5 say they like the new menu. The school has 560 students. Estimate how many students in the school like the new menu.

  1. 70
  2. 2800
  3. 490
Show answer

70 The result is 70.

Check 11

In a random sample of 25 people, 10 own a bike. What percentage of the sample own a bike?

  1. 40
  2. 10
  3. 0.4
Show answer

40 The result is 40.

Check 12

A school wants to know how its 900 students travel to school. Which method is best? A: Ask the 30 students in the bus queue. B: Number all 900 students and use random numbers to pick 40 students to ask. C: Ask the students in one Year 7 class.

  1. B
  2. A
  3. C
Show answer

B The result is B.

Check 13

In a fair random sample of 40 students, 14 say they like the new menu. The school has 800 students. Estimate how many students in the school like the new menu.

  1. 280
  2. 11200
  3. 520
Show answer

280 The result is 280.

Check 14

In a random sample of 50 people, 35 own a bike. What percentage of the sample own a bike?

  1. 70
  2. 35
  3. 0.7
Show answer

70 The result is 70.

Check 15

A school has 500 students. A random sample of 35 students is taken. What percentage of the students are in the sample?

  1. 7
  2. 35
  3. 0.07
Show answer

7 The result is 7.

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