EDEXCEL GCSE MATHS · HIGHER
Exam Practice: Drawing histograms
Drawing histograms · Further statistics · Lesson 4 of 6 · 15 marks · 30 minutes
|
Name |
|
Date |
|
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 COMPLETE (3 marks)
The table shows the times, t minutes, taken by 94 customers. Frequencies: 0 < t ≤ 10: 12, 10 < t ≤ 30: 30, 30 < t ≤ 40: 26, 40 < t ≤ 60: 18, 60 < t ≤ 100: 8. Work out the frequency density for each class.
|
|
|
|
|
|
|
|
(Total for Question 1 = 3 marks)
Question 2 COMPLETE THE HISTOGRAM (3 marks)
The table shows information about the ages, a years, of 94 people: 0 < a ≤ 10: 8, 10 < a ≤ 20: 20, 20 < a ≤ 40: 36, 40 < a ≤ 60: 30. Complete the histogram.
|
|
|
|
|
|
|
|
(Total for Question 2 = 3 marks)
Question 3 WORK OUT (2 marks)
A class 5 < x ≤ 25 has frequency 40. Work out the frequency density.
|
|
|
|
|
|
(Total for Question 3 = 2 marks)
Question 4 WORK OUT (2 marks)
A histogram bar for the class 10 < x ≤ 14 has a frequency density of 3. Work out the frequency of the class.
|
|
|
|
|
|
(Total for Question 4 = 2 marks)
Question 5 EXPLAIN (2 marks)
Explain why the height of a bar in a histogram is not the frequency when the class widths are unequal.
|
|
|
|
|
|
(Total for Question 5 = 2 marks)
Question 6 DRAW (3 marks)
Describe how to draw a histogram from a grouped frequency table with unequal class widths.
|
|
|
|
|
|
|
|
(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 15 MARKS
|
|
Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
1.2, 1.5, 2.6, 0.9, 0.2
• Class widths M1
• At least three correct M1
• All correct A1
Question 2 (3 marks)
Frequency density = 30 ÷ 20 = 1.5; a bar drawn from 40 to 60 of height 1.5.
• Frequency density 1.5 M1
• Bar from 40 to 60 A1
• Height 1.5 A1
Question 3 (2 marks)
40 ÷ 20 = 2
• Class width 20 M1
• 2 A1
Question 4 (2 marks)
Width 4; frequency = 4 × 3 = 12
• Uses 4 × 3 M1
• 12 A1
Question 5 (2 marks)
The area of a bar shows the frequency, so a wider class needs a lower bar for the same frequency. The height is the frequency density.
• Area shows frequency M1
• Frequency density used for the height C1
Question 6 (3 marks)
Work out the class width and then the frequency density for each class. Draw a frequency density scale on the vertical axis and the data on the horizontal axis. Draw touching bars with heights equal to the frequency densities.
• Frequency density B1
• Axes correctly labelled B1
• Touching bars with correct heights B1