Draw a scatter diagram of the data. Use 1 cm to represent 1 hour and 1 cm to represent 10 km.

Write down for this set of data the mean time, \(\bar t\).

Write down for this set of data the mean distance, \(\bar d\).

Mark and label the point \(M(\bar t,{\text{ }}\bar d)\) on your scatter diagram.

Draw the line of best fit on your scatter diagram.

Using your graph, estimate the time when Alex and Kris pass the 85 km distance marker. Give your answer correct to one decimal place.

Write down the equation of the regression line for the data given.

Using your equation calculate the distance marker passed by the cyclists at 10.3 hours.

Is this estimate of the distance reliable? Give a reason for your answer.

     (A1)(A2)

Notes: Award (A1) for axes labelled with d and t and correct scale, (A2) for 6 or 7 points correctly plotted, (A1) for 4 or 5 points, (A0) for 3 or less points correctly plotted. Award at most (A1)(A1) if points are joined up. If axes are reversed award at most (A0)(A2)

[3 marks]

\(\bar t = 4\)     (G1)

[1 mark]

\(\bar d = 81.1\left( {\frac{{568}}{7}} \right)\)     (G1)

Note: If answers are the wrong way around award in (i) (G0) and in (ii) (G1)(ft).

[1 mark]

Point marked and labelled with M or \(\bar t\), \(\bar d\) on their graph     (A1)(ft)(A1)(ft)

[2 marks]

Line of best fit drawn that passes through their M and (0, 48)     (A1)(ft)(A1)(ft)

Notes: Award (A1)(ft) for straight line that passes through their M, (A1) for line (extrapolated if necessary) that passes through (0, 48).

Accept error of ±3. If ruler not used award a maximum of (A1)(ft)(A0).

[2 marks]

4.5h (their answer ±0.2)     (M1)(A1)(ft)(G2)

Note: Follow through from their graph. If method shown by some indication on graph of point but answer is incorrect, award (M1)(A0).

[2 marks]

d = 8.25t + 48.1     (G1)(G1)

Notes: Award (G1) for 8.25, (G1) for 48.1.

Award at most (G1)(G0) if d = (or y =) is not seen.

Accept d – 81.1 = 8.25(t – 4) or equivalent.

[2 marks]

d = 8.25 × 10.3 + 48.1     (M1)

d = 133 km     (A1)(ft)(G2)

[2 marks]

No     (A1)

Outside the set of values of t or equivalent.     (R1)

Note: Do not award (A1)(R0).

[2 marks]

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.

This question was well answered by most of the candidates. Diagrams were in general well drawn except for some students that reversed the axes or did not use the stated scales. They were able to use the GDC to find the means and the equation of the regression line. Very few students could take the correct decision in (g) (ii) by stating that the value was outside the range of the data set. The majority inclined their answers towards the context of the question and forgot what they had been taught about how wrong extrapolation can be.