1. 1
   A histogram shows the time (in minutes) spent on homework by a group of students. The class 0–10 minutes has frequency 15. The class 10–25 minutes has frequency density 1.8. The class 25–30 minutes has frequency density 4.

   (a)

   What is the frequency density of the 0–10 minute class?

   [1 mark]

   • A1.5
   • B15
   • C1.0
   • D0.67

   (b)

   What is the frequency of the 10–25 minute class?

   [1 mark]

   • A18
   • B1.8
   • C27
   • D45

   (c)

   What is the frequency of the 25–30 minute class?

   [1 mark]

   • A120
   • B4
   • C0.8
   • D20

   Total for question 1: 3 marks

2. 2
   The masses of 100 apples are grouped for a histogram. The class 0–50g has frequency density 0.6. The class 50–90g has frequency 56.

   (a)

   Find the frequency of the 0–50g class.

   [2 marks]

   (b)

   Find the frequency density of the 50–90g class.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A histogram represents the annual salaries (in thousands of dollars) of 120 employees. The class 20–30 has frequency density 2.4. Another class, starting at 30 and ending at an unknown upper boundary w, has frequency 54 and frequency density 3.6.

   (a)

   Find the frequency of the 20–30 (thousand dollar) salary class.

   [3 marks]

   (b)

   Find the upper boundary, w, of the second class.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A histogram displays the distances (in km) travelled to work by 200 employees, grouped into unequal classes: 0–5 km: frequency density 6; 5–15 km: frequency density 8; 15–25 km: frequency density unknown; 25–40 km: frequency density 1.6.

   (a)

   Find the frequency of the 15–25 km class.

   [4 marks]

   (b)

   Using your answer to part (a), find the frequency density of the 15–25 km class.

   [4 marks]

   (c)

   Compare the frequency density of the 5–15 km class (8) with that of the 25–40 km class (1.6), and explain what this tells us about the distribution of commuting distances.

   [5 marks]

   Total for question 4: 13 marks

End of questions