Cumulative frequency and box plotsIB MYP Maths Standard: Subtopic test

1. 1
   Forty students at a school in Mumbai recorded how long they spent on homework one evening. The cumulative frequencies are: 0 students up to 10 minutes, 5 up to 20 minutes, 10 up to 30 minutes, 20 up to 40 minutes, 30 up to 50 minutes, 38 up to 60 minutes and 40 up to 70 minutes.

   (a)

   How many students spent more than 50 minutes on homework?

   [1 mark]

   • A$30$
   • B$10$
   • C$38$
   • D$2$

   (b)

   What is the median time spent on homework?

   [1 mark]

   • A$20$ minutes
   • B$30$ minutes
   • C$50$ minutes
   • D$40$ minutes

   (c)

   Find the lower quartile, the upper quartile and the interquartile range of the times.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two takeaway restaurants, X in Lagos and Y in Cairo, record their delivery times in minutes. Restaurant X: minimum 12, lower quartile 18, median 25, upper quartile 34, maximum 52. Restaurant Y: minimum 15, lower quartile 22, median 26, upper quartile 30, maximum 38.

   (a)

   What is the interquartile range of the delivery times for restaurant X?

   [1 mark]

   • A$16$ minutes
   • B$40$ minutes
   • C$25$ minutes
   • D$34$ minutes

   (b)

   Which statement about the two restaurants is correct?

   [1 mark]

   • AX has a smaller range than Y.
   • BY has a larger interquartile range than X.
   • CY's delivery times are more consistent because its interquartile range is smaller.
   • DX has a greater median than Y.

   (c)

   A customer needs a delivery within 30 minutes. Use the quartiles to explain which restaurant is more likely to deliver in time.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A courier in Singapore weighs 50 parcels. The masses $m$ (in kg) are grouped as follows: $0<m\le2$: 4 parcels; $2<m\le4$: 11 parcels; $4<m\le6$: 17 parcels; $6<m\le8$: 12 parcels; $8<m\le10$: 6 parcels.

   (a)

   Work out the cumulative frequencies and write down the coordinates you would plot on a cumulative frequency graph, starting at $(0,0)$.

   [3 marks]

   (b)

   The points are joined with straight lines. Use the graph to estimate the median mass and the interquartile range.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A coach in Sydney records the times, in seconds, of two sprinters over 20 races each. Maya: minimum 11.8, lower quartile 12.0, median 12.2, upper quartile 12.6, maximum 13.4. Jonas: minimum 11.5, lower quartile 11.9, median 12.3, upper quartile 13.0, maximum 13.2. The qualifying time for a regional meeting is 12.4 seconds.

   (a)

   (i) Calculate the range and the interquartile range for each runner.
   (ii) State, with a reason, which runner is more consistent.

   [6 marks]

   (b)

   Both sprinters qualify by running 12.4 seconds or faster. Assuming the times are evenly spread within each quarter of the data, estimate the percentage of each runner's races that were 12.4 s or faster. Justify who is more likely to qualify and state one limitation of your method.

   [6 marks]

   Total for question 4: 12 marks

End of questions