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Averages from frequency tables practice questions with answers

Foundation and Higher · Grade 4 · Calculator

A second set of averages from frequency tables 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.

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Question 1 Easy

The frequency table shows the number of siblings of each student: 1 (frequency 3), 2 (frequency 6), 3 (frequency 3), 4 (frequency 3). Work out the mean.

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Answer: 2.4

  1. Value × frequency: 1 × 3 = 3, 2 × 6 = 12, 3 × 3 = 9, 4 × 3 = 12.
  2. The total frequency is 15 and the total of value × frequency is 36.
  • Method (1): Value × frequency: 1 × 3 = 3, 2 × 6 = 12, 3 × 3 = 9, 4 × 3 = 12.
  • Accuracy (1): Answer 2.4

Question 2 Easy

The frequency table shows the number of books read by each student this month: 1 (frequency 6), 2 (frequency 1), 3 (frequency 5), 4 (frequency 5). What is the median?

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Answer: 3

  1. The total frequency is 17, so the median is the 9th value.
  2. Running total of the frequencies: 1 up to 6, 2 up to 7, 3 up to 12, 4 up to 17.
  • Method (1): The total frequency is 17, so the median is the 9th value.
  • Accuracy (1): Answer 3

Question 3 Medium

The frequency table shows the number of books read by each student this month: 1 (frequency 5), 2 (frequency 3), 3 (frequency 4), 4 (frequency 3). Work out the range.

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Answer: 3

  1. The largest value is 4 and the smallest value is 1.
  2. Range = 4 − 1.
  • Method (1): The largest value is 4 and the smallest value is 1.
  • Accuracy (1): Answer 3

Question 4 Medium

The frequency table shows the number of goals scored in each match: 0 (frequency 5), 1 (frequency 7), 2 (frequency 6), 3 (frequency 7). Work out the mean.

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Answer: 1.6

  1. Value × frequency: 0 × 5 = 0, 1 × 7 = 7, 2 × 6 = 12, 3 × 7 = 21.
  2. The total frequency is 25 and the total of value × frequency is 40.
  • Method (1): Value × frequency: 0 × 5 = 0, 1 × 7 = 7, 2 × 6 = 12, 3 × 7 = 21.
  • Accuracy (1): Answer 1.6

Question 5 Hard

The frequency table shows the number of goals scored in each match: 0 (frequency 3), 1 (frequency 2), 2 (frequency 5). Work out the mean.

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Answer: 1.2

  1. Value × frequency: 0 × 3 = 0, 1 × 2 = 2, 2 × 5 = 10.
  2. The total frequency is 10 and the total of value × frequency is 12.
  • Method (1): Value × frequency: 0 × 3 = 0, 1 × 2 = 2, 2 × 5 = 10.
  • Accuracy (1): Answer 1.2

Question 6 Hard

The frequency table shows the number of pets owned by each student: 1 (frequency 5), 2 (frequency 5), 3 (frequency 1), 4 (frequency 6), 5 (frequency 2). Work out the range.

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Answer: 4

  1. The largest value is 5 and the smallest value is 1.
  2. Range = 5 − 1.
  • Method (1): The largest value is 5 and the smallest value is 1.
  • Accuracy (1): Answer 4

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 13 marks

The frequency table shows the number of goals scored in each match: 0 (frequency 3), 1 (frequency 4), 2 (frequency 6), 3 (frequency 6), 4 (frequency 4). What is the median?

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Answer: 2

  1. The total frequency is 23, so the median is the 12th value.
  2. Running total of the frequencies: 0 up to 3, 1 up to 7, 2 up to 13, 3 up to 19, 4 up to 23.
  3. The 12th value is 2.
  • Method (1): The total frequency is 23, so the median is the 12th value.
  • Method (1): Running total of the frequencies: 0 up to 3, 1 up to 7, 2 up to 13, 3 up to 19, 4 up to 23.
  • Accuracy (1): Answer 2

Quick checks

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

Check 1

The frequency table shows the number of pets owned by each student: 1 (frequency 3), 2 (frequency 1), 3 (frequency 5), 4 (frequency 1). Work out the mean.

  1. 2.4
  2. 6
  3. 2.5
Show answer

2.4 The result is 2.4.

Check 2

The frequency table shows the number of siblings of each student: 1 (frequency 6), 2 (frequency 7), 3 (frequency 5), 4 (frequency 3). What is the median?

  1. 2
  2. 3
  3. 11
Show answer

2 The result is 2.

Check 3

The frequency table shows the number of books read by each student this month: 0 (frequency 4), 1 (frequency 5), 2 (frequency 7). What is the mode?

  1. 2
  2. 7
  3. 0
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2 The result is 2.

Check 4

The frequency table shows the number of goals scored in each match: 1 (frequency 4), 2 (frequency 5), 3 (frequency 1). Work out the mean.

  1. 1.7
  2. 5.67
  3. 2
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1.7 The result is 1.7.

Check 5

The frequency table shows the number of siblings of each student: 1 (frequency 6), 2 (frequency 5), 3 (frequency 6), 4 (frequency 5). Work out the range.

  1. 3
  2. 1
  3. 22
Show answer

3 The result is 3.

Check 6

The frequency table shows the number of books read by each student this month: 0 (frequency 7), 1 (frequency 1), 2 (frequency 1), 3 (frequency 2), 4 (frequency 3). Work out the mean.

  1. 1.5
  2. 4.2
  3. 2
Show answer

1.5 The result is 1.5.

Check 7

The frequency table shows the number of goals scored in each match: 1 (frequency 7), 2 (frequency 1), 3 (frequency 1), 4 (frequency 2). What is the median?

  1. 1
  2. 3
  3. 6
Show answer

1 The result is 1.

Check 8

The frequency table shows the number of pets owned by each student: 0 (frequency 6), 1 (frequency 1), 2 (frequency 3). What is the mode?

  1. 0
  2. 6
  3. 2
Show answer

0 The result is 0.

Check 9

The frequency table shows the number of books read by each student this month: 1 (frequency 3), 2 (frequency 3), 3 (frequency 6), 4 (frequency 2). Work out the mean.

  1. 2.5
  2. 4.5
  3. 12.5
Show answer

2.5 The result is 2.5.

Check 10

The frequency table shows the number of goals scored in each match: 0 (frequency 5), 1 (frequency 3), 2 (frequency 7), 3 (frequency 3), 4 (frequency 2). Work out the range.

  1. 4
  2. 5
  3. 20
Show answer

4 The result is 4.

Check 11

The frequency table shows the number of pets owned by each student: 0 (frequency 1), 1 (frequency 7), 2 (frequency 2). Work out the mean.

  1. 1.1
  2. 3.67
  3. 1
Show answer

1.1 The result is 1.1.

Check 12

The frequency table shows the number of siblings of each student: 1 (frequency 1), 2 (frequency 2), 3 (frequency 7), 4 (frequency 1). What is the median?

  1. 3
  2. 5
  3. 13
Show answer

3 The result is 3.

Check 13

The frequency table shows the number of goals scored in each match: 0 (frequency 7), 1 (frequency 5), 2 (frequency 6). What is the mode?

  1. 0
  2. 7
  3. 2
Show answer

0 The result is 0.

Check 14

The frequency table shows the number of pets owned by each student: 0 (frequency 4), 1 (frequency 7), 2 (frequency 7), 3 (frequency 4). Work out the mean.

  1. 1.5
  2. 3.5
  3. 11.5
Show answer

1.5 The result is 1.5.

Check 15

The frequency table shows the number of siblings of each student: 1 (frequency 4), 2 (frequency 6), 3 (frequency 2). Work out the range.

  1. 2
  2. 4
  3. 12
Show answer

2 The result is 2.

Keep going with Averages from frequency tables

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