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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.

[1]
a.

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.

[4]
b.

Write down

(i)     the mean distance, ˉx, of the trees from the river bank;

(ii)     the mean circumference, ˉy, of the trees.

[2]
c.

Plot and label the point M(ˉx, ˉy) on your graph.

[2]
d.

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.

[4]
e.

Draw the regression line y on x on your graph.

[2]
f.

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.

[2]
g.

Markscheme

continuous     (A1)

[1 mark]

a.

     (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]

b.

(i)     26 (m)     (A1)

(ii)     65 (cm)     (A1)

[2 marks]

c.

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]

 

d.

(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=0.756281x+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]

e.

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]

f.

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]

g.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
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d.
[N/A]
e.
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f.
[N/A]
g.

Syllabus sections

Topic 4 - Statistical applications » 4.3 » The regression line for y on x.
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