StatisticsIB MYP Maths Standard: Topic test

1. 1
   A radio station in Buenos Aires wants to find out what music its $12\,000$ listeners prefer. It posts a survey on its website and uses the first $200$ replies it receives.

   (a)

   What is the main reason this sample may be biased?

   [1 mark]

   • AA sample of $200$ is far too large to be reliable.
   • BOnly listeners who use the website and reply quickly can take part.
   • CThe listeners were chosen at random from a list.
   • DThe survey collects categorical data.

   (b)

   Which method would give the least biased sample of $200$ listeners?

   [1 mark]

   • AAsk the first $200$ people who walk into the station's building.
   • BAsk $200$ people at a rock concert.
   • CAsk $200$ of the station's staff.
   • DChoose $200$ listeners using random numbers from a list of all $12\,000$ listeners.

   (c)

   The station plans to ask: “Most people love pop music. Do you agree?” State one problem with this question and write an improved question.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A school in Auckland asks $120$ pupils how they usually travel to school. The results are: walk $30$, bus $45$, car $15$ and bike $30$.

   (a)

   A pie chart is drawn for this data. What angle represents the pupils who travel by bus?

   [1 mark]

   • A$135^\circ$
   • B$45^\circ$
   • C$90^\circ$
   • D$120^\circ$

   (b)

   Which statement about the pie chart is correct?

   [1 mark]

   • AThe car sector is $90^\circ$.
   • BThe bus sector is $120^\circ$.
   • CThe walk sector and the bike sector are each $90^\circ$.
   • DThe car sector is larger than the bike sector.

   (c)

   State one advantage of a bar chart and one advantage of a pie chart for showing this data.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student recorded the number of text messages she sent on each of $9$ days: $14,\ 9,\ 22,\ 9,\ 17,\ 31,\ 9,\ 12,\ 18$.

   (a)

   Find the median, the mode and the range of the number of messages.

   [3 marks]

   (b)

   (i) Calculate the mean number of messages, to $1$ decimal place. (ii) On a tenth day she sends $x$ messages and the mean for the $10$ days is exactly $16$. Find $x$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Ana and Ben are basketball players. Their points in each of $8$ games are: Ana $12,\ 14,\ 15,\ 15,\ 16,\ 17,\ 18,\ 19$ and Ben $4,\ 10,\ 15,\ 16,\ 18,\ 22,\ 25,\ 30$.

   (a)

   (i) Calculate Ana's mean. (ii) Find the median points for each player. (iii) Find the range for each player.

   [6 marks]

   (b)

   Ben's mean is $17.5$ points. The coach must choose one player for a final in which a reliable score matters more than a high score. Compare the two players using averages and spread, and recommend one of them with a justified conclusion.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   The finishing times of $80$ runners in a $10$ km race in Doha are summarised using a cumulative frequency graph. Its readings are: lower quartile $38$ minutes, median $44$ minutes and upper quartile $52$ minutes.

   (a)

   Which cumulative frequency value is used to read off the lower quartile from the graph?

   [1 mark]

   • A$40$
   • B$60$
   • C$20$
   • D$80$

   (b)

   What is the interquartile range of the finishing times?

   [1 mark]

   • A$14$ minutes
   • B$6$ minutes
   • C$8$ minutes
   • D$90$ minutes

   (c)

   Estimate how many runners took longer than $52$ minutes.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A gardener in Auckland measures the height $y$ cm of a bean plant at the end of each of weeks $1$ to $8$, with $x$ the number of weeks. The points rise steadily from lower left to upper right, very close to a straight line. The line of best fit passes through the points $(2,12)$ and $(6,36)$.

   (a)

   Which statement describes the correlation between the number of weeks and the height?

   [1 mark]

   • AStrong negative correlation
   • BNo correlation
   • CWeak positive correlation
   • DStrong positive correlation

   (b)

   Use the line of best fit to estimate the height at the end of week $4$.

   [1 mark]

   • A$18$ cm
   • B$24$ cm
   • C$30$ cm
   • D$42$ cm

   (c)

   The gardener uses the line to predict the height of the plant at week $40$. Explain why this prediction is unreliable.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   The daily maximum temperatures in July (in $^\circ$C) in two cities are summarised over $31$ days. Muscat: lowest $31$, lower quartile $35$, median $38$, upper quartile $41$, highest $46$. Cairo: lowest $30$, lower quartile $33$, median $35$, upper quartile $37$, highest $40$.

   (a)

   Calculate the range and the interquartile range of the temperatures in Muscat.

   [3 marks]

   (b)

   Compare the temperatures in the two cities. Refer to the median and to the spread in your answer.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A bike-hire scheme in Medellin records the length $t$ minutes of $100$ journeys: $0<t\le10$: $15$ journeys; $10<t\le20$: $30$; $20<t\le30$: $35$; $30<t\le40$: $15$; $40<t\le50$: $5$.

   (a)

   (i) State the modal class. (ii) Estimate the mean journey time, to $1$ decimal place. (iii) State the class that contains the median and explain why your answer to (ii) is only an estimate.

   [6 marks]

   (b)

   The scheme states that fewer than a quarter of journeys last longer than $30$ minutes and so need an extra charge. (i) Write down the cumulative frequency for $t\le30$. (ii) Estimate the median by linear interpolation within its class, assuming the times in a class are evenly spread. Give your answer to $1$ decimal place. (iii) Estimate the percentage of journeys longer than $30$ minutes and decide whether the data support the scheme's statement.

   [6 marks]

   Total for question 8: 12 marks

End of questions