Date | May 2014 | Marks available | 4 | Reference code | 14M.2.sl.TZ1.1 |
Level | SL only | Paper | 2 | Time zone | TZ1 |
Command term | Write down | Question number | 1 | Adapted from | N/A |
Question
As part of his IB Biology field work, Barry was asked to measure the circumference of trees, in centimetres, that were growing at different distances, in metres, from a river bank. His results are summarized in the following table.
State whether distance from the river bank is a continuous or discrete variable.
On graph paper, draw a scatter diagram to show Barry’s results. Use a scale of 1 cm to represent 5 m on the x-axis and 1 cm to represent 10 cm on the y-axis.
Write down
(i) the mean distance, ˉx, of the trees from the river bank;
(ii) the mean circumference, ˉy, of the trees.
Plot and label the point M(ˉx, ˉy) on your graph.
Write down
(i) the Pearson’s product–moment correlation coefficient, r, for Barry’s results;
(ii) the equation of the regression line y on x, for Barry’s results.
Draw the regression line y on x on your graph.
Use the equation of the regression line y on x to estimate the circumference of a tree that is 40 m from the river bank.
Markscheme
continuous (A1)
[1 mark]
(A1)(A1)(A1)(A1)
Notes: Award (A1) for labelled axes and correct scales; if axes are reversed award (A0) and follow through for their points. Award (A1) for at least 3 correct points, (A2) for at least 6 correct points, (A3) for all 9 correct points. If scales are too small or graph paper has not been used, accuracy cannot be determined; award (A0). Do not penalize if extra points are seen.
[4 marks]
(i) 26 (m) (A1)
(ii) 65 (cm) (A1)
[2 marks]
point M labelled, in correct position (A1)(A1)(ft)
Notes: Award (A1)(ft) for point plotted in correct position, (A1) for point labelled M or (ˉx, ˉy). Follow through from their answers to part (c).
[2 marks]
(i) −0.988 (−0.988432…) (G2)
Note: Award (G2) for −0.99. Award (G1) for −0.990.
Award (A1)(A0) if minus sign is omitted.
(ii) y=−0.756x+84.7 (y=−0.756281…x+84.6633…) (G2)
Notes: Award (A1) for −0.756x, (A1) for 84.7. If the answer is not given as an equation, award a maximum of (A1)(A0).
[4 marks]
regression line through their M (A1)((ft)
regression line through their (0,85) (accept 85±1) (A1)(ft)
Notes: Follow through from part (d). Award a maximum of (A1)(A0) if the line is not straight. Do not penalize if either the line does not meet the y-axis or extends into quadrants other than the first.
If M is not plotted or labelled, then follow through from part (c).
Follow through from their y-intercept in part (e)(ii).
[2 marks]
−0.756281(40)+84.6633 (M1)
=54.4 (cm) (54.4120…) (A1)(ft)(G2)
Notes: Accept 54.5 (54.46) for use of 3 sf. Accept 54.3 from use of −0.76 and 84.7.
Follow through from their equation in part (e)(ii) irrespective of working shown; the final answer seen must be consistent with that equation for the final (A1) to be awarded.
Do not accept answers taken from the graph.
[2 marks]