EXM.1.SL.TZ0.3

pestleMathematicsAISLPaper 1EXM· sl-4-10-spearmans-rank-correlation-coefficientsource ↗

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]

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

[1]

Calculate Spearman’s rank correlation coefficient for this data.

[6]

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

[1]

Markscheme / solution

the data is not linear R1

[1 mark]

the data is (montonically) decreasing. R1

[1 mark]

assign ranks M1

average equal prices M1

A1A1

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

[6 marks]

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

[1 mark]

Examiners’ report

[N/A]