Scatter graphs and correlationIB MYP Maths Standard: Subtopic test

1. 1
   A café in Cape Town records the maximum temperature $x$ (in °C) and the number $y$ of cold drinks sold on six days: $(18,40)$, $(21,55)$, $(24,68)$, $(27,85)$, $(30,98)$, $(33,115)$. A line of best fit for the data passes through $(20,45)$ and $(30,100)$.

   (a)

   Which statement describes the correlation between temperature and drinks sold?

   [1 mark]

   • AStrong negative correlation
   • BNo correlation
   • CStrong positive correlation
   • DWeak positive correlation

   (b)

   Use the line of best fit to estimate the number of drinks sold when the maximum temperature is 26 °C.

   [1 mark]

   • A$78$
   • B$143$
   • C$71$
   • D$89$

   (c)

   Find the gradient of the line of best fit and explain what it means in this context.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Eight students record the hours $x$ of revision they did before a test and the number $y$ of mistakes they made: $(1,19)$, $(2,16)$, $(3,14)$, $(4,13)$, $(5,10)$, $(6,8)$, $(7,7)$, $(8,4)$. A line of best fit for the data passes through $(2,16)$ and $(6,8)$.

   (a)

   Which statement describes the correlation between hours of revision and mistakes made?

   [1 mark]

   • AStrong positive correlation
   • BWeak positive correlation
   • CNo correlation
   • DStrong negative correlation

   (b)

   A student revises for 10 hours. Why would using the line of best fit to predict this student's mistakes be unreliable?

   [1 mark]

   • AThe correlation is negative.
   • B10 hours is outside the range of the data (1 to 8 hours), so the prediction is an extrapolation.
   • CA line of best fit can only predict values that are already in the data.
   • DThe line of best fit passes through only two of the points.

   (c)

   Use the line of best fit to estimate the number of mistakes made by a student who revises for 5.5 hours.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A road-safety team in Dubai records the speed $x$ (in km/h) and the braking distance $y$ (in metres) of a car in six trials: $(20,8)$, $(30,14)$, $(40,19)$, $(50,25)$, $(60,30)$, $(70,36)$. A line of best fit for the data passes through $(20,8)$ and $(70,36)$.

   (a)

   Find the mean speed and the mean braking distance, and write down the coordinates of the mean point, through which a line of best fit should pass.

   [3 marks]

   (b)

   Find the equation of the line of best fit. Use it to estimate the braking distance at 55 km/h. Explain why an estimate at 120 km/h would be unreliable.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A health researcher in Manila records the hours $x$ of exercise per week and the resting heart rate $y$ (in beats per minute) of eight adults: $(0,81)$, $(1,77)$, $(2,75)$, $(4,69)$, $(5,64)$, $(6,63)$, $(7,58)$, $(8,57)$. A line of best fit for the data passes through $(0,80)$ and $(8,56)$. A gym advertises: 'Exercise 20 hours a week and your resting heart rate drops to the level shown by this line.'

   (a)

   (i) Describe the correlation, in context.
   (ii) Find the equation of the line of best fit.
   (iii) Estimate the resting heart rate of an adult who exercises for 4.5 hours a week.

   [6 marks]

   (b)

   Evaluate the gym's advertisement. Use the equation of the line and give reasons for your judgement.

   [6 marks]

   Total for question 4: 12 marks

End of questions