4.2 Presenting dataIB Maths: Applications and Interpretation HL: Subtopic test

1. 1
   The masses, $m$ kg, of 50 parcels at a depot are recorded. $0<m\le2$: 4 parcels; $2<m\le4$: 11 parcels; $4<m\le6$: 17 parcels; $6<m\le8$: 12 parcels; $8<m\le10$: 6 parcels.

   (a)

   How many parcels have a mass of 6 kg or less?

   [1 mark]

   • A17
   • B15
   • C44
   • D32

   (b)

   Which is the modal class?

   [1 mark]

   • A$4<m\le6$
   • B$6<m\le8$
   • C$2<m\le4$
   • D$8<m\le10$

   (c)

   Find the percentage of parcels with a mass greater than 8 kg.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   The heights of 100 plants in a greenhouse are summarised by cumulative frequency. 8 plants have height at most 10 cm, 30 plants at most 20 cm, 68 plants at most 30 cm, 92 plants at most 40 cm and all 100 plants at most 50 cm. Assume that the cumulative frequency rises uniformly (in a straight line) between these heights.

   (a)

   How many plants are taller than 30 cm?

   [1 mark]

   • A68
   • B8
   • C32
   • D24

   (b)

   Which is the best estimate of the median height?

   [1 mark]

   • A50 cm
   • B25.3 cm
   • C30 cm
   • D20 cm

   (c)

   Estimate the number of plants with height between 15 cm and 35 cm.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two cafés record the number of customers each day. Café A: minimum 35, lower quartile 48, median 60, upper quartile 72, maximum 91. Café B: minimum 30, lower quartile 50, median 58, upper quartile 66, maximum 110.

   (a)

   Find the interquartile range (IQR) and the range of each café.

   [3 marks]

   (b)

   Show that the maximum for Café B is an outlier. Hence compare the two distributions, using the median and the IQR.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A teacher records the time, $t$ minutes, taken by 60 students in Class A to finish a test. $10\le t<20$: 4 students; $20\le t<30$: 11 students; $30\le t<40$: 19 students; $40\le t<50$: 16 students; $50\le t<60$: 10 students. Assume the times are spread uniformly within each class interval. For Class B, the summary is: minimum 14, lower quartile 29, median 37, upper quartile 45, maximum 60.

   (a)

   (i) Write down the cumulative frequency for each class of Class A.
   (ii) Estimate the median time.
   (iii) Estimate the lower and upper quartiles, and hence the IQR.

   [6 marks]

   (b)

   (i) Show that Class B has no outliers.
   (ii) Compare the median and IQR of the two classes.
   (iii) Use the symmetry of the box and whiskers that the summary of Class B would give to decide whether its times may be normally distributed.

   [6 marks]

   Total for question 4: 12 marks

End of questions