EDEXCEL GCSE MATHS · HIGHER
Exam Practice: Interpreting histograms
Interpreting histograms · Further statistics · Lesson 5 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 USE THE HISTOGRAM (4 marks)
The histogram gives information about the ages of visitors to a museum. (a) Work out the number of visitors aged 10 to 20. (b) Work out an estimate for the number of visitors aged 25 to 40.
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(Total for Question 1 = 4 marks)
Question 2 WORK OUT (2 marks)
Use the same histogram to work out the total number of visitors.
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(Total for Question 2 = 2 marks)
Question 3 ESTIMATE (3 marks)
Use the same histogram to find an estimate for the median age.
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(Total for Question 3 = 3 marks)
Question 4 ESTIMATE (3 marks)
Use the same histogram to find an estimate for the mean age of the visitors.
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(Total for Question 4 = 3 marks)
Question 5 WORK OUT (2 marks)
A histogram bar for a class of width 20 has height 1.4. Work out the frequency of the class.
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(Total for Question 5 = 2 marks)
Question 6 EXPLAIN (2 marks)
Explain why the answer to part (b) of the first question is only an estimate.
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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)
(a) 10 × 3 = 30. (b) 15 × 2.2 = 33.
• 10 × 3 M1
• 30 A1
• 15 × 2.2 M1
• 33 A1
Question 2 (2 marks)
16 + 30 + 44 + 24 + 10 = 124
• All five frequencies M1
• 124 A1
Question 3 (3 marks)
Median position 62; running total 46 after age 20; 62 − 46 = 16; 16 ÷ 2.2 = 7.27; median ≈ 27.3.
• Median position 62 B1
• Interpolates in the class 20 to 40 M1
• 27.3 (accept 27 to 27.5) A1
Question 4 (3 marks)
(16 × 5 + 30 × 15 + 44 × 30 + 24 × 55 + 10 × 80)/124 = 3970/124 = 32.0
• Midpoints times frequencies M1
• 3970 A1
• 32.0 A1
Question 5 (2 marks)
20 × 1.4 = 28
• Uses 20 × 1.4 M1
• 28 A1
Question 6 (2 marks)
The data are grouped, so we do not know how the values are spread inside the class. We assumed they are evenly spread.
• Data grouped M1
• Assumes even spread C1