EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Comparing and describing distributions
Comparing and describing distributions · Further statistics · Lesson 6 of 6 · 14 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 cumulative frequency graphs show the times taken by 60 people in Group A and 60 people in Group B to complete a puzzle. Compare the times taken by the two groups.
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(Total for Question 1 = 4 marks)
Question 2 COMPARE (2 marks)
Boys: median 12.4 s, interquartile range 1.2 s. Girls: median 13.1 s, interquartile range 2.0 s. Write down two comparisons.
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(Total for Question 2 = 2 marks)
Question 3 COMPARE (2 marks)
Set A has mean 24 and range 10. Set B has mean 21 and range 25. Compare the two sets.
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(Total for Question 3 = 2 marks)
Question 4 DESCRIBE (2 marks)
A distribution has a mean of 30 and a median of 25. Describe the skew of the distribution.
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(Total for Question 4 = 2 marks)
Question 5 EXPLAIN (2 marks)
A data set has one very large outlier. Explain why the median is a better average than the mean.
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(Total for Question 5 = 2 marks)
Question 6 EXPLAIN (2 marks)
The mean time for pupils in a London school is lower than in a school in Leeds. Ben says every pupil in the London school must be faster than every pupil in Leeds. Explain why Ben is wrong.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 14 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 (about 22) is lower than for A (about 28), so B were quicker on average. The IQRs are similar (B about 17, A about 16), so the spread is similar.
• Median for each read from the graph M1
• Comment on average in context A1
• IQR for each read from the graph M1
• Comment on spread in context A1
Question 2 (2 marks)
On average the boys were faster (12.4 s against 13.1 s). The boys' times were more consistent (IQR 1.2 s against 2.0 s).
• Average compared in context B1
• Spread compared in context B1
Question 3 (2 marks)
Set A has a higher mean (24 against 21). Set A has a smaller range (10 against 25), so it is more consistent.
• Compares means B1
• Compares ranges B1
Question 4 (2 marks)
The mean is greater than the median, so the distribution has positive skew (a long tail to the right).
• Mean above median M1
• Positive skew A1
Question 5 (2 marks)
The outlier pulls the mean up but has almost no effect on the median, so the median better represents the typical value.
• Mean affected by outlier M1
• Median not affected C1
Question 6 (2 marks)
The mean is only an average. Some pupils in the London school could be slower than some in Leeds; the data may be spread widely.
• Mean is an average only M1
• Individual values may overlap C1