EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Cumulative frequency
Cumulative frequency · Further statistics · Lesson 2 of 6 · 15 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 USE THE GRAPH (4 marks)
The cumulative frequency graph shows the times, in minutes, taken by 80 students to complete a puzzle. Use the graph to find an estimate for (a) the median (b) the interquartile range.
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(Total for Question 1 = 4 marks)
Question 2 USE THE GRAPH (2 marks)
Use the same graph of the times taken by 80 students to estimate how many students took more than 45 minutes.
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(Total for Question 2 = 2 marks)
Question 3 COMPLETE (2 marks)
The table shows the times taken by 60 students. Frequencies: 0 < t ≤ 10: 4, 10 < t ≤ 20: 11, 20 < t ≤ 30: 20, 30 < t ≤ 40: 16, 40 < t ≤ 50: 7, 50 < t ≤ 60: 2. Work out the cumulative frequencies.
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(Total for Question 3 = 2 marks)
Question 4 EXPLAIN (2 marks)
Explain why the points on a cumulative frequency graph are plotted at the upper class boundaries.
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(Total for Question 4 = 2 marks)
Question 5 DRAW (3 marks)
Describe how to draw a cumulative frequency graph from a table of grouped data.
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(Total for Question 5 = 3 marks)
Question 6 WORK OUT (2 marks)
A cumulative frequency graph shows the lower quartile is 20 and the upper quartile is 36. Work out the interquartile range and explain what it tells you.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 15 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (4 marks)
(a) Median at 40: about 30 minutes. (b) LQ at 20: about 21; UQ at 60: about 38; IQR about 17. Accept readings within 1 minute.
• Median: reads across at 40 M1
• 30 (accept 29 to 31) A1
• LQ and UQ read at 20 and 60 M1
• IQR about 17 A1
Question 2 (2 marks)
About 72 students took 45 minutes or less, so 80 − 72 = 8 took more. Accept 7 to 9.
• Reads about 72 at 45 M1
• 80 − 72 = 8 A1
Question 3 (2 marks)
4, 15, 35, 51, 58, 60
• At least 3 correct M1
• All correct A1
Question 4 (2 marks)
The cumulative frequency counts everyone up to the end of each class, so the running total is only known at the upper boundary.
• Cumulative frequency includes the whole class M1
• Only true at the upper boundary C1
Question 5 (3 marks)
Work out the running totals. Plot each total against the upper class boundary, plus a point at 0 for the lowest boundary. Join the points with a smooth curve.
• Running totals B1
• Plot at upper boundaries B1
• Smooth curve B1
Question 6 (2 marks)
36 − 20 = 16. The middle half of the data lie within a range of 16.
• 16 B1
• The spread of the middle 50% C1