IB Maths AI SL 4.10 Spearman's Rank Correlation

IB Mathematics: applications and interpretation guide, first assessment 2021

Practise assigning and averaging ranks, calculating Spearman's coefficient and interpreting the strength and direction of monotonic association while considering ties and outliers.

How this is tested

rank both variables consistently and assign average ranks to tied observations
calculate Spearman's coefficient from paired ranks with technology or rank differences
interpret sign and magnitude as monotonic association and compare its suitability with Pearson correlation

[Maximum number: 4]

Aiden works for WoodCraft Wonders, a company that makes wooden letters. He wants to predict the demand for different letters. He thinks that letters earlier in the alphabet are more popular.
Aiden finds that, in the year he was born, his name was the most popular in the United States. From the 10 most popular boys' names, his name was first alphabetically. This data is shown in the following table.

Table for Question 2(a) — IB Maths AI SL

Aiden calculates the Spearman's rank correlation coefficient, $r_{s}$ , for this data.

Find $r_{s}$ , and use the following table to interpret its value.

How this is tested

Question 2(a)