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Date May Specimen paper Marks available 2 Reference code SPM.2.SL.TZ0.3
Level Standard Level Paper Paper 2 Time zone Time zone 0
Command term Write down Question number 3 Adapted from N/A

Question

The Malvern Aquatic Center hosted a 3 metre spring board diving event. The judges, Stan and Minsun awarded 8 competitors a score out of 10. The raw data is collated in the following table.

The Commissioner for the event would like to find the Spearman’s rank correlation coefficient.

Write down the value of the Pearson’s product–moment correlation coefficient, r .

[2]
a.i.

Using the value of r , interpret the relationship between Stan’s score and Minsun’s score.

[2]
a.ii.

Write down the equation of the regression line y on x .

[2]
b.

Use your regression equation from part (b) to estimate Minsun’s score when Stan awards a perfect 10.

[2]
c.i.

State whether this estimate is reliable. Justify your answer.

[2]
c.ii.

Copy and complete the information in the following table.

[2]
d.

Find the value of the Spearman’s rank correlation coefficient, r s .

[2]
e.i.

Comment on the result obtained for r s .

[2]
e.ii.

The Commissioner believes Minsun’s score for competitor G is too high and so decreases the score from 9.5 to 9.1.

Explain why the value of the Spearman’s rank correlation coefficient r s does not change.

[1]
f.

Markscheme

0.909 (0.909181…)      A2

[2 marks]

a.i.

(very) strong and positive        A1A1

Note: Award A1 for (very) strong A1 for positive.

[2 marks]

a.ii.

y = 1.14 x + 0.578 ( y = 1.14033 x + 0.578183 )        A1A1

Note: Award A1 for 1.14 x , A1 for 0.578 . Award a maximum of A1A0 if the answer is not an equation in the form y = m x + c .

[2 marks]

b.

1.14 × 10 + 0.578       M1

12.0 (11.9814…)        A1

[2 marks]

c.i.

no the estimate is not reliable       A1

outside the known data range         R1
OR
a score greater than 10 is not possible               R1

Note: Do not award A1R0.

[2 marks]

c.ii.

     A1A1

Note: Award A1 for correct ranks for Stan. Award A1 for correct ranks for Minsun.

[2 marks]

d.

0.933  (0.932673…)      A2

[2 marks]

e.i.

Stan and Minsun strongly agree on the ranking of competitors.         A1A1

Note: Award A1 for “strongly agree”, A1 for reference to a rank order.

[2 marks]

e.ii.

decreasing the score to 9.1, does not change the rank of competitor G       A1

[1 mark]

f.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x
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Topic 4—Statistics and probability » SL 4.10—Spearman’s rank correlation coefficient
Topic 4—Statistics and probability

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