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Cambridge IGCSE Maths (0580) · Topic 9: Statistics · 9.3

Cambridge IGCSE Maths 0580 Averages and Measures of Spread Questions

Averages and Measures of Spread questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.

Practise averages and measures of spread →Averages and Measures of Spread notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Averages and Measures of Spread questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

Find the mean, median, mode and range of \(8, \ 3, \ 9, \ 4, \ 8, \ 12, \ 5\).

Show the worked answer
  1. Mean: \(\frac{8 + 3 + 9 + 4 + 8 + 12 + 5}{7} = \frac{49}{7} = 7\).
  2. In order: \(3, 4, 5, 8, 8, 9, 12\); median \(= 8\) (the 4th value).
  3. Mode \(= 8\). Range \(= 12 - 3 = 9\).

Answer: Mean \(7\), median \(8\), mode \(8\), range \(9\)

Question 2 Core calculator · easy · 2 marks

Find the mean of \(3.2, \ 4.8, \ 5.1, \ 2.9, \ 4.0\).

Show the answer and mark scheme
  • M1 20 ÷ 5
  • A1 4

Answer: \(4\)

Question 3 Core non-calculator · medium

The table shows the number of goals scored in \(20\) matches.
Find (a) the mean (b) the median (c) the mode.

Goals01234
Frequency36542
Show the worked answer
  1. (a) Total goals: \(0 \times 3 + 1 \times 6 + 2 \times 5 + 3 \times 4 + 4 \times 2 = 36\). Mean \(= 36 \div 20 = 1.8\).
  2. (b) The 10th and 11th values: running totals \(3, 9, 14\), so both are \(2\). Median \(= 2\).
  3. (c) Highest frequency: \(1\) goal.

Answer: (a) \(1.8\) (b) \(2\) (c) \(1\)

Question 4 Core non-calculator · medium

The mean of five numbers is \(12\). Four of the numbers are \(10\), \(15\), \(8\) and \(14\).
Find the fifth number.

Show the worked answer
  1. Total of five numbers \(= 5 \times 12 = 60\).
  2. \(60 - (10 + 15 + 8 + 14) = 60 - 47 = 13\)

Answer: \(13\)

Question 5 Core non-calculator · medium · 2 marks

The table shows the number of goals scored by a team in 20 matches.

\[\begin{array}{c|cccc} \text{Goals} & 0 & 1 & 2 & 3 \\ \hline \text{Frequency} & 4 & 6 & 7 & 3 \end{array}\]

Find (a) the mode (b) the median.

Show the answer and mark scheme
  • B1 (a) 2
  • B1 (b) 1.5

Answer: (a) \(2\) (b) \(1.5\)

Question 6 Core calculator · medium · 3 marks

The table shows the number of pets owned by 25 students.

\[\begin{array}{c|ccccc} \text{Pets} & 0 & 1 & 2 & 3 & 4 \\ \hline \text{Frequency} & 7 & 9 & 5 & 3 & 1 \end{array}\]

Calculate the mean number of pets.

Show the answer and mark scheme
  • M1 0×7 + 1×9 + 2×5 + 3×3 + 4×1 (= 32)
  • M1 their 32 ÷ 25
  • A1 1.28

Answer: \(1.28\)

Question 7 Core non-calculator · hard

The mean of six numbers is \(9\). One number is removed and the mean of the other five is \(8\).
Which number was removed?

Show the worked answer
  1. Total of six: \(6 \times 9 = 54\). Total of five: \(5 \times 8 = 40\).
  2. Removed number \(= 54 - 40 = 14\).

Answer: \(14\)

Averages and Measures of Spread questions: Extended

Extended content, for Papers 2 and 4. Core students can skip these.

Question 8 Extended non-calculator · medium

Find the lower quartile, upper quartile and interquartile range of
\(3, \ 5, \ 6, \ 8, \ 9, \ 11, \ 12, \ 15, \ 17, \ 20, \ 22\)

Show the worked answer
  1. There are \(11\) values in order. The median is the 6th value, \(11\).
  2. Lower quartile: the median of the lower five, the 3rd value, \(6\). Upper quartile: the 9th value, \(17\).
  3. IQR \(= 17 - 6 = 11\).

Answer: LQ \(6\), UQ \(17\), IQR \(11\)

Question 9 Extended calculator · hard

The table shows the times, \(t\) minutes, that \(20\) people took to finish a puzzle.
(a) Calculate an estimate of the mean time.
(b) Write down the modal class.

Time (t minutes)0 < t ≤ 1010 < t ≤ 2020 < t ≤ 3030 < t ≤ 40
Frequency4952
Show the worked answer
  1. (a) Midpoints \(5, 15, 25, 35\): \(5 \times 4 + 15 \times 9 + 25 \times 5 + 35 \times 2 = 20 + 135 + 125 + 70 = 350\).
  2. Estimated mean \(= 350 \div 20 = 17.5\) minutes.
  3. (b) The class with the highest frequency, \(9\).

Answer: (a) \(17.5\) minutes (b) \(10 \lt t \le 20\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).

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Questions students ask

Which Cambridge 0580 papers can test averages and measures of spread?

Averages and Measures of Spread is on both tiers (syllabus 9.3), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.

Where can I practise more averages and measures of spread questions?

In the 0580 practice for topic 9 (Statistics), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.

More statistics questions