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  • Perplex
    IB Math AISL
    /
    Bivariate Statistics
    /

    Problems

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    Problem Bank - Bivariate Statistics

    Access custom-built, exam-style problems for bivariate statistics. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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    IB: 6
    10

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    The number of daylight hours H at noon in City X was measured on the 21st of each month for eight consecutive months (m=1 for January, …, m=8 for August). The results are shown below; the value for May (m=5) was lost in transcription.

    Month (m)

    1

    2

    3

    4

    5

    6

    7

    8

    Daylight (h)

    8.5

    9.5

    10.5

    11.5

    —

    13.5

    14.5

    15.5

    Assuming the data follows a linear model over this period, find the regression line of H on m for the seven known points.

    1. Use your line to estimate the daylight hours on the 21st of May (m=5).

      [2]
    2. Explain why your line should not be used to estimate the month m at which H=17.0h.

      [2]
    3. Explain in context why your line should not be used to predict the daylight hours on the 21st of December (m=12).

      [2]
    4. State a more appropriate model for H over an entire year. You are not expected to calculate any parameters.

      [1]
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    Lucy operates a smoothie stall and has observed that warmer temperatures lead to higher sales of her smoothies. Over six days she recorded the maximum daily temperature, T(°C), and the number of smoothies sold, S. The results are:

    T(°C)

    14

    16

    18

    20

    22

    24

    S sold

    118

    132

    140

    155

    165

    158

    The relationship between S and T is modeled by the regression line S=aT+b.

    1. Find the values of a and b.

      [3]
    2. Write down the correlation coefficient r.

      [1]
    3. Using your regression equation, estimate the number of smoothies sold when T=21°C.

      [2]
    4. Interpret the value of the slope a in the context of the problem.

      [1]
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