EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Statistical Diagrams 2
Statistical diagrams 2 · Interpreting and representing data · Lesson 6 of 6 · 11 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [3 marks]
Here are the times, in seconds, that 12 students took to solve a puzzle: 23, 35, 41, 28, 32, 45, 38, 26, 31, 40, 36, 29. Draw an ordered stem-and-leaf diagram to show this information.
Question 2 NON-CALCULATOR [2 marks]
For the puzzle times in the last question, find (a) the median (b) the range.
Question 3 NON-CALCULATOR [2 marks]
A second group of students solved the same puzzle. Their median time was 38 seconds and their range was 15 seconds. Compare the times of the two groups.
Question 4 NON-CALCULATOR [2 marks]
A company used this graph in an advert to show that its sales had "soared". Give two reasons why the graph is misleading.
Question 5 NON-CALCULATOR [2 marks]
The table shows the heights, h cm, of 25 plants. 0 < h ≤ 10: 3 plants. 10 < h ≤ 20: 8 plants. 20 < h ≤ 30: 10 plants. 30 < h ≤ 40: 4 plants. Write down the coordinates of the points you would plot to draw a frequency polygon.
Answers
Check your answer only once you have written one.
Question 1 [3 marks]
Stem 2: 3 6 8 9. Stem 3: 1 2 5 6 8. Stem 4: 0 1 5. Key: 2 then 3 means 23 seconds.
▸ A correct stem-and-leaf diagram with the leaves in order B2
▸ A correct diagram with the leaves not in order, or one error B1
▸ A correct key B1
Question 2 [2 marks]
(a) In order: 23, 26, 28, 29, 31, 32, 35, 36, 38, 40, 41, 45. The median is (32 + 35)/2 = 33.5 seconds. (b) 45 − 23 = 22 seconds.
▸ (a) 33.5 B1
▸ (b) 22 B1
Question 3 [2 marks]
The first group had a lower median (33.5 s against 38 s), so on average they solved the puzzle faster. The second group had a smaller range (15 s against 22 s), so their times were more consistent.
▸ A correct comparison of the medians, in context C1
▸ A correct comparison of the ranges, in context C1
Question 4 [2 marks]
The vertical axis does not start at zero, so the increase looks much bigger than it is. The vertical axis has no label or units, and the scale is uneven.
▸ One valid reason, e.g. the axis does not start at 0 C1
▸ A second valid reason, e.g. no axis label, or an uneven scale C1
Question 5 [2 marks]
(5, 3), (15, 8), (25, 10), (35, 4)
▸ All four points correct B2
▸ Midpoints correct, or at least two points correct B1