Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Cumulative Frequency & Box Plots — exam questions
10 original Incandio exam-style questions on cumulative Frequency & Box Plots, 26 marks, about 31 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.
This is the practice set for Cumulative Frequency & Box Plots — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.
What these questions ask of you
6 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.
- Write down (1–2 marks)
- a value that needs no working — read off, recalled or stated
- Work out (1–5 marks)
- a calculated result, with the working that produced it
- Explain why (1–2 marks)
- one short justification — mathematics almost never asks for extended explanation
- Find (1–5 marks)
- a value or expression obtained by a method the learner chooses
- Show that (2–5 marks)
- every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
- Calculate (1–5 marks)
- a numerical answer obtained by calculation
Assessed on Paper 1 and Paper 2.
Where these sit in the specification
Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 6.1. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.
The 10 questions
Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.
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(1)Write down
Write down the number of parcels with a mass of 10 kg or less.
Masses of 80 parcels Mass m (kg) Frequency 0 < m ≤ 5 9 5 < m ≤ 10 17 10 < m ≤ 15 26 15 < m ≤ 20 20 20 < m ≤ 25 8 (Total for Question 1 = 1 mark)
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(2)Work out
Work out the cumulative frequency for parcels of mass 20 kg or less.
Masses of 80 parcels Mass m (kg) Frequency 0 < m ≤ 5 9 5 < m ≤ 10 17 10 < m ≤ 15 26 15 < m ≤ 20 20 20 < m ≤ 25 8 cumulative frequency = ............................
(Total for Question 2 = 2 marks)
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(2)Write down
There are 120 test scores. Write down the cumulative frequency at which the median should be read, and the median score itself.
Readings taken from a cumulative frequency curve for 120 test scores Cumulative frequency Score 30 44 60 52 90 61 108 70 (Total for Question 3 = 2 marks)
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(1)Explain why
A student plots each cumulative frequency at the midpoint of its group. Explain why the points should be plotted at the upper boundary instead.
(Total for Question 4 = 1 mark)
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(3)Find
Using the readings from the curve for the 120 test scores, find the interquartile range.
Readings taken from a cumulative frequency curve for 120 test scores Cumulative frequency Score 30 44 60 52 90 61 108 70 (Total for Question 5 = 3 marks)
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(3)Show that
Show that 10 per cent of the 120 test scores were above 70.
Readings taken from a cumulative frequency curve for 120 test scores Cumulative frequency Score 30 44 60 52 90 61 108 70 (Total for Question 6 = 3 marks)
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(3)Work out
Work out an estimate for the number of test scores between 52 and 61.
Readings taken from a cumulative frequency curve for 120 test scores Cumulative frequency Score 30 44 60 52 90 61 108 70 (Total for Question 7 = 3 marks)
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(2)Calculate
A box plot has its whiskers at 12 and 48, the ends of its box at 20 and 38, and its median line at 27. Calculate the interquartile range and the range.
(Total for Question 8 = 2 marks)
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(4)Find
Using the parcel masses, find the group that contains the upper quartile, and state how many parcels lie in the groups above it.
Masses of 80 parcels Mass m (kg) Frequency 0 < m ≤ 5 9 5 < m ≤ 10 17 10 < m ≤ 15 26 15 < m ≤ 20 20 20 < m ≤ 25 8 (Total for Question 9 = 4 marks)
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(5)Work out
Table 3 shows the times taken by 80 runners. Work out an estimate of the median and of the interquartile range.
Table 3 — times taken by 80 runners to complete a course. Time t (minutes) Frequency 20 < t ≤ 25 6 25 < t ≤ 30 18 30 < t ≤ 35 26 35 < t ≤ 40 20 40 < t ≤ 45 10 median and interquartile range = ............................ minutes
(Total for Question 10 = 5 marks)
Have them marked, then defend the answer
Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.
- Mark these questions — 10 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
- Teach it — explain cumulative Frequency & Box Plots to Ember, an AI pupil who does not have it yet and asks the awkward question.
- Defend it — argue it against Adolphe Quetelet over three rounds, marked against descriptors you can read first.
Completely free. No subscriptions, no paywalls, no account needed to start.
Back to the module
- Cumulative Frequency & Box Plots — Running totals, medians and quartiles read from the curve, box plots, and comparing distributions properly. Higher Tier.
- All of Incandio Mathematics · Incandio Exam Practice