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Date	May Example question	Marks available	6	Reference code	EXM.1.SL.TZ0.3
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Calculate	Question number	3	Adapted from	N/A

Question

Charles wants to measure the strength of the relationship between the price of a house and its distance from the city centre where he lives. He chooses houses of a similar size and plots a graph of price, $P$ (in thousands of dollars) against distance from the city centre, $d$ (km).

The data from the graph is shown in the table.

Explain why it is not appropriate to use Pearson’s product moment correlation coefficient to measure the strength of the relationship between $P$ and $d$ .

[1]

a.

Explain why it is appropriate to use Spearman’s rank correlation coefficient to measure the strength of the relationship between $P$ and $d$ .

[1]

b.

Calculate Spearman’s rank correlation coefficient for this data.

[6]

c.

State what conclusion Charles can make from the answer in part (c).

[1]

d.

Markscheme

the data is not linear R1

[1 mark]

a.

the data is (montonically) decreasing. R1

[1 mark]

b.

assign ranks M1

average equal prices M1

A1A1

${r_s} = - 0.991$ (Note: condone ${r_s} = 0.991$ ) A2

[6 marks]

c.

There is a strong, negative relationship between the price of a house and its distance from the city centre. R1

[1 mark]

d.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

Syllabus sections

Topic 4—Statistics and probability » SL 4.10—Spearman’s rank correlation coefficient

Show 30 related questions

22M.2.SL.TZ1.3e.i:
Find the value of the Spearman’s rank correlation coefficient $r_{s}$ .
EXM.1.SL.TZ0.2a:
Calculate Spearman’s rank correlation coefficient for this data.
22M.2.SL.TZ1.3d.i:
$a$ .
22M.2.SL.TZ1.3d.ii:
$b$ .
22M.2.SL.TZ1.3d.iii:
$c$ .
22M.2.SL.TZ1.3e.ii:
Interpret the value obtained for $r_{s}$ .
22M.2.SL.TZ1.3f:
When calculating the ranks, Chester incorrectly read the Netherlands’ score as $478$ . Explain why the value of the Spearman’s rank correlation $r_{s}$ does not change despite this error.
EXN.2.AHL.TZ0.3c:
Find the value of the $χ^{2}$ test statistic $(χ_{c a l c}^{2})$ for this test.
21M.2.SL.TZ1.1i.i:
Calculate the value of $r_{s}$ .
EXM.1.SL.TZ0.2b:
State what conclusion Kayla can make from the answer in part (a).
EXM.1.SL.TZ0.3d:
State what conclusion Charles can make from the answer in part (c).
EXM.1.SL.TZ0.3a:
Explain why it is not appropriate to use Pearson’s product moment correlation coefficient to measure the strength of the relationship between $P$ and $d$ .
SPM.2.SL.TZ0.3f:
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.
SPM.2.SL.TZ0.3a.ii:
Using the value of $r$ , interpret the relationship between Stan’s score and Minsun’s score.
SPM.2.SL.TZ0.3d:
Copy and complete the information in the following table.
SPM.2.SL.TZ0.3c.ii:
State whether this estimate is reliable. Justify your answer.
SPM.2.SL.TZ0.3e.ii:
Comment on the result obtained for ${r_s}$ .
SPM.2.SL.TZ0.3c.i:
Use your regression equation from part (b) to estimate Minsun’s score when Stan awards a perfect 10.
SPM.2.SL.TZ0.3e.i:
Find the value of the Spearman’s rank correlation coefficient, ${r_s}$ .
SPM.2.SL.TZ0.3b:
Write down the equation of the regression line $y$ on $x$ .
21M.2.SL.TZ1.1i.ii:
Interpret your result.
SPM.2.SL.TZ0.3a.i:
Write down the value of the Pearson’s product–moment correlation coefficient, $r$ .
EXM.1.SL.TZ0.3b:
Explain why it is appropriate to use Spearman’s rank correlation coefficient to measure the strength of the relationship between $P$ and $d$ .
EXN.2.SL.TZ0.1c:
Which of the correlation coefficients would you recommend is used to assess whether or not there is an association between total number of minutes late and distance from school? Fully justify your answer.
21M.2.SL.TZ1.1h:
Copy and complete the information in the following table.
21M.3.AHL.TZ1.2c.i:
Without calculation, explain why it might not be appropriate to calculate a correlation coefficient for the whole sample of $18$ employees.
21M.3.AHL.TZ1.2c.ii:
Find $r_{s}$ for the seven employees working in the international department.
21M.3.AHL.TZ1.2c.iii:
Hence comment on the validity of the written assessment as a measure of the level of performance of employees in this department. Justify your answer.
EXN.2.AHL.TZ0.3d:
Determine the degrees of freedom for Dana’s test.
EXN.2.AHL.TZ0.3e:
It is given that the critical value for this test is $9.49$ .

State the conclusion of the test in context. Use your answer to part (c) to justify your conclusion.

Hide related questions

Topic 4—Statistics and probability