1. 1
   The times, in minutes, spent by 50 customers in a shop were grouped as follows: $0 \leq t < 10$ (class width 10) - frequency 15; $10 \leq t < 25$ (class width 15) - frequency 30; $25 \leq t < 40$ (class width 15) - frequency 5.

   (a)

   Find the frequency density of the class $0 \leq t < 10$.

   [1 mark]

   • A1.5
   • B1.0
   • C15
   • D0.67

   (b)

   Find the frequency density of the class $10 \leq t < 25$.

   [1 mark]

   • A0.5
   • B1.5
   • C30
   • D2.0

   (c)

   Find the frequency density of the class $25 \leq t < 40$, correct to 2 decimal places.

   [1 mark]

   • A0.67
   • B0.33
   • C5.00
   • D1.33

   Total for question 1: 3 marks

2. 2
   A histogram represents the masses, in kg, of 60 parcels. The class $0 \leq m < 5$ (class width 5) has frequency density 4, and the class $5 \leq m < 20$ (class width 15) contains the remaining parcels.

   (a)

   Find the frequency of parcels in this class.

   [2 marks]

   (b)

   Find the frequency density of the class $5 \leq m < 20$, correct to 2 decimal places.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A survey of 80 plants recorded their heights, in cm, in two unequal groups: $10 \leq h < 30$ (class width 20) has frequency density 1.2, and $30 \leq h < 70$ (class width 40) contains the rest.

   (a)

   Find the frequency of plants in the class $10 \leq h < 30$.

   [3 marks]

   (b)

   Find the frequency density of the class $30 \leq h < 70$.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A histogram shows the ages, in years, of 100 members of a gym in four classes: $10 \leq a < 20$ (width 10) has frequency density 1.5; $20 \leq a < 30$ (width 10) has frequency density 3.2; $30 \leq a < 50$ (width 20) has frequency density $d$; $50 \leq a < 70$ (width 20) has frequency density 0.65.

   (a)

   Find the frequencies of the first, second and fourth classes, and hence find the frequency of the class $30 \leq a < 50$.

   [4 marks]

   (b)

   Find the frequency density $d$ for the class $30 \leq a < 50$.

   [4 marks]

   (c)

   State the modal class based on frequency density, and explain why using raw frequency alone would give a misleading modal class in this case.

   [5 marks]

   Total for question 4: 13 marks

End of questions