Cumulative Frequency: GCSE and IGCSE Maths Practice
Grouped and continuous data diagrams
Cumulative Frequency
33 self-marking GCSE and IGCSE practice questions on Cumulative Frequency, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Extended tier. Instant marking with full worked solutions on every question.
A few of the 33 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 7-8
A table shows call-answering times for 90 calls at a call centre:
Sam draws a cumulative frequency graph for this data. His curve starts at the point (0,4), and every point is plotted at the middle of its class interval.
(a) Write down one thing that is wrong with Sam's graph.
(b) Write down a second, different thing that is wrong with Sam's graph.
What are the common mistakes in Cumulative Frequency?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Uses a class boundary value directly instead of interpolating within the class
Read off the upper class boundary of the class containing the median position, without interpolating within the class
Reads a cumulative frequency value as if it were the ordinary (individual class) frequency
Gave the individual class frequency for that class instead of the running cumulative total up to that boundary
Compares cumulative totals not subgroup counts
Compared the cumulative frequency TOTALS at age 60 and 50 (38 vs 22) directly, instead of first finding the actual number of people IN their 50s and IN their 60s by subtracting consecutive cumulative frequencies.
Quick answers about Cumulative Frequency
How many Cumulative Frequency practice questions are there?
There are 33 self-marking GCSE and IGCSE Maths questions on Cumulative Frequency, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Extended tier. Each one is marked instantly and has a full worked solution.
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No. You can start practising Cumulative Frequency straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
Show the worked solution
A correct cumulative frequency graph always starts at (0,0) - before any data is counted, the cumulative frequency must be 0. Sam's curve incorrectly starts at (0,4). A1
Each cumulative frequency point should be plotted at the UPPER boundary of its class interval (e.g. (10,4), (20,25), (30,70)), not at the middle of the interval. A2
Question 24 marksGrade 7-8
75 people attend a clinic. Their ages are recorded on a cumulative frequency graph:
A nurse says: "More than twice as many people are in their 60s as in their 50s."
Is she correct? Show working to support your answer.
Show the worked solution
People in their 50s: 22−10=12... wait - using the correct class boundaries: people aged 50 to 60 (50<age⩽60): 38−22=16M1
People in their 60s (60<age⩽70): 60−38=22M2
Double the 50s count: 2×16=32M3
Since 22<32, the nurse is NOT correct. A1
Question 34 marksGrade 8
A fitness centre records how long each customer spends in the gym. This cumulative frequency table summarises the results:
Time (t minutes)
Cumulative frequency
t≤10
6
t≤20
24
t≤30
35
t≤40
48
t≤50
60
t≤60
74
Calculate an estimate of the mean time the customers spend in the gym.