Histograms: Fluency and Exam Drill - Worksheets, Questions and Revision

12 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

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GCSE · Statistics

7.16D Histograms: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 50 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A histogram has a class 10-20 with frequency density 3. Work out the frequency for the class 10-20.
(Total for Question 1 is 1 mark)
2
A histogram has classes 0-5, 5-15 and 15-25. The class widths are 5, 10 and 10. The frequency densities are 4, 2.5 and 3 respectively.
Work out the frequency of the class 5-15.
(Total for Question 2 is 2 marks)
3
A histogram has three classes 0-4, 4-9 and 9-14. The frequency density for 0-4 is 2 and for 9-14 is 3. The total number of observations is 40.
Find the frequency density of the class 4-9.
(Total for Question 3 is 3 marks)
4
The histogram below has three bars:
0-6 width 6 with frequency density 2,
6-14 width 8 with frequency density 1.25,
14-20 width 6 with frequency density 1.5.
Estimate the frequency of the class 6-14.
Figure (to be drawn): Three histogram bars for intervals 0-6 (density 2), 6-14 (density 1.25), 14-20 (density 1.5). Not to scale.
(Total for Question 4 is 1 mark)
5
A class 20-35 has frequency 45. Work out the frequency density for the class 20-35.
(Total for Question 5 is 2 marks)
6
The histogram shows three classes:
0-10 width 10 with density 1 (frequency 10),
10-25 width 15 with density 2 (frequency 30),
25-40 width 15 with density 1.6 (frequency 24).
Estimate the median value.
Figure (to be drawn): Histogram with classes 0-10 (density 1), 10-25 (density 2), 25-40 (density 1.6). Not to scale.
(Total for Question 6 is 3 marks)
7
A histogram has classes:
0-10 density 1.2,
10-20 density 1.5,
20-40 density 0.8.
Use the histogram to estimate the mean. Give your answer correct to one decimal place.
Figure (to be drawn): Histogram with classes 0-10 (density 1.2), 10-20 (density 1.5), 20-40 (density 0.8). Not to scale.
(Total for Question 7 is 4 marks)
8
The class 50-80 has width 30 and frequency 90. Show that the frequency density for 50-80 is 3.
(Total for Question 8 is 2 marks)
9
A histogram has classes 0-5 (density 4) and 5-15 (density 2).
Estimate the number of observations with 3 ≤ x < 8.
Figure (to be drawn): Two histogram bars: 0-5 density 4, 5-15 density 2. Not to scale.
(Total for Question 9 is 3 marks)
10
A histogram has classes:
0-10 density 1 (frequency 10),
10-30 density 2 (frequency 40),
30-? density 3 (frequency unknown).
The total number of observations is 80.
Find the upper boundary of the last class.
(Total for Question 10 is 3 marks)
11
A histogram has classes:
0-10 density 2,
10-25 density 4,
25-45 density d.
The midpoints are 5, 17.5 and 35 respectively.
The mean of the whole distribution is 20.
Find the frequency of the final class.
Figure (to be drawn): Histogram with classes 0-10 (density 2), 10-25 (density 4), 25-45 (density d). Not to scale.
(Total for Question 11 is 4 marks)
12
A histogram has classes:
A: 0-10 density 3,
B: 10-20 density 2,
C: 20-50 density 1.2.
Which class has the largest frequency density and which class has the largest frequency? Give both answers.
(Total for Question 12 is 2 marks)
Mark scheme · 7.16D Histograms: Fluency and Exam Drill

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12