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Scatter Plots and Two-Way Tables: math test solutions, Grade 8 – download the PDF

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Test solutions Grade 8 : Scatter Plots and Two-Way Tables — Zyro the alien explorer of Planète Maths

Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

1 Reading a scatter plot / 4 pts

  1. Positive association: more months of training, more commands. (1 pt)
  2. The outlier is \((7, 3)\); for example, that puppy missed many sessions or was sick. (1 pt)
  3. The point at \(x = 4\) is \((4, 5)\): 5 commands. (1 pt)
  4. Points with \(y \geq 7\): \((5, 7)\), \((6, 8)\), \((8, 10)\): 3 puppies. (1 pt)

2 Equation of a trend line / 4 pts

  1. \(m = \dfrac{32 - 14}{8 - 2} = \dfrac{18}{6} = 3\). (1 pt)
  2. \(14 = 3(2) + b\), so \(b = 8\). \(y = 3x + 8\). (1 pt)
  3. About 3 dollars are saved each week. (1 pt)
  4. At the start (week 0), the model predicts 8 dollars already saved. (1 pt)

3 Making predictions / 3 pts

  1. \(1.2(10) + 3 = 15\) miles. (1 pt)
  2. \(1.2x + 3 = 21\), \(1.2x = 18\), \(x = 15\). Week 15. (1 pt)
  3. No: week 60 gives \(1.2(60) + 3 = 75\) miles, which is not realistic. This is extrapolation far outside the data. (1 pt)

4 Breakfast and lateness / 4 pts

  1. Row totals 90 and 60; column totals 27 and 123; grand total 150. (1 pt)
  2. \(\dfrac{9}{90} = 10\%\) and \(\dfrac{18}{60} = 30\%\). (1.5 pts)
  3. The percents differ a lot, so there is an association: students who skip breakfast are more often late in this sample. (1.5 pts)

5 True or false? / 3 pts

  1. False: it only needs to follow the trend, and its y-intercept can be any value. (1 pt)
  2. False: a third factor can affect both variables. (1 pt)
  3. True: an outlier pulls the line toward it. (1 pt)

6 Residual check / 2 pts

  1. \(2(7) + 1 = 15\). The actual value 5 is \(15 - 5 = 10\) below the prediction. (1 pt)
  2. The line would be pulled down toward the point and become flatter, because this outlier is far below the pattern. (1 pt)
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