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

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H16D Histograms and Frequency Density: Fluency and Exam Drill

EDEXCEL 1ST0 · Calculator allowed · about 50 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A class in a grouped frequency table has frequency 18 and class width 3. Work out the frequency density for this class.
(Total for Question 1 is 1 mark)
2
A class has frequency 40 and class width 8. Work out the frequency density for this class.
(Total for Question 2 is 1 mark)
3
A class has frequency density 4 and class width 7. Work out the frequency for this class.
(Total for Question 3 is 1 mark)
4
A class has frequency density 3.5 and class width 6. Work out the frequency for this class.
(Total for Question 4 is 1 mark)
5
A class has frequency 54 and frequency density 9. Work out the class width for this class.
(Total for Question 5 is 1 mark)
6
A class has frequency 33 and frequency density 5.5. Work out the class width for this class.
(Total for Question 6 is 1 mark)
7
A class has frequency density 2.4 and class width 5. Work out the frequency for this class.
(Total for Question 7 is 1 mark)
8
Write down whether the following statement is True or False: In a histogram, the area of a bar represents the frequency for that class.
(Total for Question 8 is 1 mark)
9
A class has frequency 96 and class width 12. Work out the frequency density for this class.
(Total for Question 9 is 2 marks)
10
A class has frequency density 3.25 and class width 8. Work out the frequency for this class.
(Total for Question 10 is 2 marks)
11
A class has frequency 51 and frequency density 8.5. Work out the class width for this class.
(Total for Question 11 is 2 marks)
12
A class has frequency density 2.8 and class width 15. Work out the frequency for this class.
(Total for Question 12 is 2 marks)
13
A class has frequency 91 and class width 13. Work out the frequency density for this class.
(Total for Question 13 is 2 marks)
14
A class has frequency density 6.5 and frequency 78. Work out the class width for this class.
(Total for Question 14 is 2 marks)
15
A cafe manager records the waiting time, w minutes, of 90 customers using unequal class widths. The class 0 < w ≤ 5 has frequency 25. A second class, 5 < w ≤ 15, has the same frequency density as the first class. Work out the frequency for the second class.
(Total for Question 15 is 3 marks)
16
A gardener records the height, h cm, of 120 seedlings using unequal class widths, because most seedlings are a similar height but a few are much taller. The class 0 < h ≤ 10 has frequency 18. The class 10 < h ≤ 40 has frequency density 2.2. Work out how many of the 120 seedlings are NOT in these two classes.
(Total for Question 16 is 3 marks)
17
A vet records the mass, m kg, of some dogs using a grouped frequency table with unequal class widths, shown below.
Mass, m (kg)FrequencyClass widthFrequency density
0 < m ≤ 101210?
10 < m ≤ 25?152.4
25 < m ≤ 401215?

Work out the frequency density for the class 0 < m ≤ 10, the frequency for the class 10 < m ≤ 25, and the frequency density for the class 25 < m ≤ 40.
(Total for Question 17 is 3 marks)
18
A forestry researcher records the age, y years, of 100 trees using a histogram with unequal class widths. Three of the four classes are: 0 < y ≤ 20 with frequency density 1.5; 20 < y ≤ 40 with frequency density 2.0; 40 < y ≤ 70 with frequency density 0.6. Given that the total frequency for all 100 trees is shared across all four classes, work out the frequency for the missing fourth class.
(Total for Question 18 is 3 marks)
19
A factory tests the lifetime, t hours, of 200 batteries using a histogram with unequal class widths, because most batteries fail within a similar time but a few last much longer. The class 0 < t ≤ 50 has frequency density 0.6. The class 50 < t ≤ 150 has frequency density 1.28. Show that the number of batteries lasting more than 50 hours is 128, and hence find the probability that a randomly chosen battery from this sample lasts more than 50 hours. Give your answer as a decimal.
(Total for Question 19 is 4 marks)
20
A market trader sells umbrellas and records his sales on a histogram with unequal class widths. He says: 'The tallest bar on my histogram is for umbrellas priced 15 pounds to 20 pounds, so I sold more umbrellas in that price range than in any other.' The class 15 < p ≤ 20 has frequency density 9. The class 20 < p ≤ 45 has frequency density 3. Work out the number of umbrellas sold in each of these two price ranges, and use your answers to evaluate the trader's claim.
(Total for Question 20 is 4 marks)
Mark scheme · H16D Histograms and Frequency Density: 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

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

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Question 1

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Question 2

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Question 3

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Question 4

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Question 5

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Question 6

1 mark

Question 7

1 mark

Question 8

1 mark

Question 9

2 marks

Question 10

2 marks

Question 11

2 marks

Question 12

2 marks

Question 13

2 marks

Question 14

2 marks

Question 15

3 marks

Question 16

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Question 17

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Question 18

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Question 19

4 marks

Question 20

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