HistogramsIB MYP Maths Extended: Subtopic test

1. 1
   A café in Seoul records how long $t$ minutes 70 customers wait to be served. The results are: $0<t\le2$: 8 customers; $2<t\le5$: 21 customers; $5<t\le10$: 30 customers; $10<t\le20$: 11 customers. The data is to be shown in a histogram.

   (a)

   What is the frequency density of the class $2<t\le5$?

   [1 mark]

   • A$63$
   • B$21$
   • C$7$
   • D$10.5$

   (b)

   Which class has the tallest bar in the histogram?

   [1 mark]

   • A$5<t\le10$, because it has the most customers
   • B$2<t\le5$
   • C$0<t\le2$
   • D$10<t\le20$

   (c)

   Find the frequency density of the class $10<t\le20$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student investigates classes of different widths that each have frequency 12. The class $0<x\le1$ (width 1) has frequency density 12. The class $1<x\le3$ (width 2) has frequency density 6. The class $3<x\le7$ (width 4) has frequency density 3. The class $7<x\le15$ (width 8) has frequency density 1.5.

   (a)

   A class of width 16 also has frequency 12. What is its frequency density?

   [1 mark]

   • A$192$
   • B$1.33$ (to 3 s.f.)
   • C$28$
   • D$0.75$

   (b)

   Which rule describes the pattern in the data?

   [1 mark]

   • Afrequency $=$ frequency density $\times$ class width
   • Bfrequency $=$ frequency density $\div$ class width
   • Cfrequency $=$ frequency density $+$ class width
   • Dfrequency $=$ class width $\div$ frequency density

   (c)

   Use the rule to find the frequency of a class of width 6 with frequency density 2.5, and the frequency density of a class of width 3 with the same frequency.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A histogram shows the ages $a$ in years of the people who visited a museum in Cape Town on one day. The frequency densities are: $0\le a<10$: 2.4; $10\le a<20$: 3.5; $20\le a<40$: 4.2; $40\le a<70$: 1.5.

   (a)

   Find the number of visitors in each class and the total number of visitors.

   [3 marks]

   (b)

   Estimate the number of visitors who were younger than 30.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A school asks 120 students how long, $t$ minutes, they spend on homework one evening. The results are: $0<t\le15$: 18 students; $15<t\le30$: 30 students; $30<t\le60$: 45 students; $60<t\le120$: 27 students. A newsletter says: 'More than half of our students spend over 30 minutes on homework.'

   (a)

   (i) Find the frequency density of each class.
   (ii) State which class has the tallest bar in the histogram.
   (iii) Estimate the number of students who spend more than 45 minutes on homework.

   [6 marks]

   (b)

   The student council says that the class $15<t\le30$ contains the most students because it has the tallest bar. Explain why the council is wrong, and use the data to evaluate the newsletter's claim.

   [6 marks]

   Total for question 4: 12 marks

End of questions