EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Box plots
Box plots · Further statistics · Lesson 3 of 6 · 16 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 COMPARE (4 marks)
The box plots show the marks of the students in Class A and in Class B in a test. Compare the distributions of the marks.
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(Total for Question 1 = 4 marks)
Question 2 WORK OUT (3 marks)
Here are nine numbers: 5, 8, 10, 12, 13, 15, 19, 22, 26. Work out the median and the interquartile range.
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(Total for Question 2 = 3 marks)
Question 3 DRAW (3 marks)
The five-number summary of some data is: minimum 12, lower quartile 20, median 27, upper quartile 35, maximum 50. Describe how to draw the box plot.
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(Total for Question 3 = 3 marks)
Question 4 WORK OUT (2 marks)
A box plot has minimum 12, lower quartile 20, median 27, upper quartile 35 and maximum 50. Work out the range and the interquartile range.
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(Total for Question 4 = 2 marks)
Question 5 EXPLAIN (2 marks)
The box plot for 60 people has a median of 40. How many of the 60 people have a value greater than 40?
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(Total for Question 5 = 2 marks)
Question 6 EXPLAIN (2 marks)
Give one reason why the interquartile range is a better measure of spread than the range.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 16 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (4 marks)
The median for B (32) is higher than for A (30), so B did slightly better on average. The IQR for B (13) is less than for A (18), so B's marks were more consistent.
• Compares medians with values M1
• Conclusion about average in context A1
• Compares IQR or range with values M1
• Conclusion about spread in context A1
Question 2 (3 marks)
Median = 13. LQ = 9, UQ = 20.5, IQR = 20.5 − 9 = 11.5.
• Median 13 B1
• LQ 9 and UQ 20.5 M1
• 11.5 A1
Question 3 (3 marks)
Draw a number line. Draw a box from 20 to 35 with a line inside at 27. Draw whiskers from the box to 12 and to 50.
• Box from 20 to 35 B1
• Median line at 27 B1
• Whiskers to 12 and 50 B1
Question 4 (2 marks)
Range = 50 − 12 = 38; IQR = 35 − 20 = 15.
• 38 B1
• 15 B1
Question 5 (2 marks)
30, because the median splits the data in half.
• 30 B1
• Median splits the data in half C1
Question 6 (2 marks)
The range depends on the extreme values, so one unusual value changes it. The interquartile range is not affected by extreme values.
• Range affected by extremes M1
• IQR uses only the middle half A1