Data presentation and diagramsAQA A-Level Maths: Subtopic test

1. 1
   A histogram shows the times, in minutes, taken to serve 80 customers. The classes are 0 to 2, 2 to 5, 5 to 10 and 10 to 20 minutes, with frequency densities 10, 8, 4 and 1.6 respectively.

   (a)

   How many customers are in the class 2 to 5 minutes?

   [1 mark]

   • A8
   • B24
   • C11
   • D2.7

   (b)

   Assuming the customers in each class are spread evenly, estimate how many were served in under 4 minutes.

   [1 mark]

   • A28
   • B32
   • C44
   • D36

   (c)

   Estimate the number of customers who took longer than 8 minutes to be served.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A histogram shows the distances, in km, that commuters travel to work. For the class 10 to 15 km the frequency density is 6, for 15 to 25 km it is 3.5, and for 25 to 45 km it is 0.6.

   (a)

   How many commuters are in the class 10 to 15 km?

   [1 mark]

   • A6
   • B5
   • C30
   • D1.2

   (b)

   How many more commuters are in the class 10 to 15 km than in the class 25 to 45 km?

   [1 mark]

   • A18
   • B5.4
   • C42
   • D30

   (c)

   A student says: 'The bar for 10 to 15 km is the tallest of the three, so more commuters travel 10 to 15 km than travel 15 to 25 km.' Is the student correct? Justify your answer.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The times, in seconds, taken by 100 pupils to complete a puzzle are recorded in classes. The frequencies are 10 for 0 to 20, 30 for 20 to 30, 40 for 30 to 40, 15 for 40 to 60 and 5 for 60 to 100 seconds.

   (a)

   Find the frequency densities for the classes 0 to 20, 40 to 60 and 60 to 100 seconds.

   [3 marks]

   (b)

   A pupil is chosen at random. Assuming the times are spread evenly within each class, estimate the probability that the pupil took between 25 and 50 seconds.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The waiting times, $T$ minutes, of 100 customers at a service counter are recorded in the classes $0\le T<5$, $5\le T<10$, $10\le T<20$ and $20\le T<40$, with frequencies 20, 40, 30 and 10 respectively. A histogram is drawn with relative frequency density (frequency $\div$ 100 $\div$ class width) on the vertical axis, and is used as a model for the waiting time of a randomly chosen customer.

   (a)

   (i) Find the heights of the four bars.
   (ii) State the total area of the bars and explain why it takes this value.
   (iii) Use the model to find $P(8<T<15)$.

   [6 marks]

   (b)

   (i) Use the model to estimate how many of the 100 customers waited 30 minutes or more.
   (ii) A student draws the histogram with the frequencies 20, 40, 30 and 10 as the bar heights. Explain why this is misleading.
   (iii) The manager claims that at least 75% of customers wait less than 12 minutes. Evaluate this claim using the model.

   [6 marks]

   Total for question 4: 12 marks

End of questions