Representing dataIB MYP Maths Extended: Subtopic test

1. 1
   A class of 30 students chose their favourite sport: football 12, swimming 8, tennis 6 and other sports 4.

   (a)

   In a pie chart of this data, what is the angle for football?

   [1 mark]

   • A$144^\circ$
   • B$120^\circ$
   • C$72^\circ$
   • D$12^\circ$

   (b)

   In a pictogram, one symbol stands for $2$ students. How many symbols are needed for swimming?

   [1 mark]

   • A$8$
   • B$16$
   • C$2$
   • D$4$

   (c)

   Maria says that a line graph is the best way to show this data. Explain why she is wrong and suggest a better representation.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Eleven students scored these marks in a test: 34, 41, 45, 38, 52, 47, 41, 36, 58, 45 and 41. The marks are shown in an ordered stem-and-leaf diagram with stems 3, 4 and 5. The key is 4 | 1 means 41.

   (a)

   Which row of leaves is correct for stem 4 in the ordered diagram?

   [1 mark]

   • A$1\ 5\ 7$
   • B$1\ 5\ 7\ 1\ 5\ 1$
   • C$1\ 1\ 1\ 5\ 5\ 7$
   • D$41\ 41\ 41\ 45\ 45\ 47$

   (b)

   What is the median mark?

   [1 mark]

   • A$38$
   • B$41$
   • C$45$
   • D$47$

   (c)

   Find the range of the marks and state one advantage of a stem-and-leaf diagram over a grouped frequency table.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A café owner records the highest temperature (in °C) and the number of cold drinks sold on six days. The pairs (temperature, drinks sold) are (14, 20), (18, 35), (21, 48), (25, 60), (28, 78) and (30, 85).

   (a)

   Describe the relationship between temperature and drinks sold, and explain why the owner should not use this data to predict sales on a day when the temperature is $40^\circ$C.

   [3 marks]

   (b)

   Find the mean point $(\bar{x},\bar{y})$, where $\bar{x}$ is the mean temperature and $\bar{y}$ is the mean number of drinks sold. Give each coordinate to $1$ decimal place.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A company's yearly profit was 4.0 million dirhams in 2021, 4.2 million in 2022, 4.3 million in 2023 and 4.5 million in 2024. In its advert, the company draws a bar chart whose vertical axis starts at 3.9 million instead of 0.

   (a)

   (i) Calculate the percentage increase in profit from 2021 to 2024.
   (ii) On the advert's bar chart, the height of each bar is measured from the axis start of $3.9$ million. How many times as tall is the 2024 bar as the 2021 bar?
   (iii) Explain why the bar chart is misleading.

   [6 marks]

   (b)

   Suggest a more suitable way to show this data fairly, explain how it should be drawn, and use the data to describe the trend in profit.

   [6 marks]

   Total for question 4: 12 marks

End of questions