Question 1.

A scientist got sick of working, so she decided to go for a holiday, but decided to conduct a trial to determine the number of sea urchins observed. She chose a line to swim each day for 13 days, and counted the number of sea urchins observed when she swam the line. She also recorded the temperature of the water in degrees Celsius.

Temperature | Sea urchin observed |

13 | 2 |

14 | 3 |

14 | 4 |

15 | 6 |

17 | 10 |

18 | 3 |

19 | 6 |

19 | 7 |

20 | 6 |

21 | 2 |

24 | 7 |

25 | 9 |

26 | 10 |

- The mean temperature for the 13 trials was .346 degrees Celsius greater then the median and on those 13 trials, a total of 75 sea urchins were observed.

The gradient of the scatter plot was m

a) Comment on the strength of the correlation between the bivariant data [2 marks]

b) Sketch a box and whisker plot [4 marks]

c) Find the gradient of the line, if it passes through the point mean of temperature and the mean of the sea urchins observed [5 marks]

d) Find the number of sea urchins expected for her final run if the temperature is 21 degrees Celsius [1 mark]

Question 2.

2020 HSC Math Q27

Answer.

a) Weak, positive, r^2 about 0.4

b)

c) m=0.39

d) 6.6, therefore, about 7