4.10 Spearman's rank correlationIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 4.10 Spearman's rank correlation

1. Six students sat a maths test and a physics test. Their marks (maths, physics) were $(45,52)$, $(60,58)$, $(72,80)$, $(38,40)$, $(55,61)$ and $(80,75)$. In both subjects the highest mark is given rank $1$.
   Interpret the value of $r_s$ in context.2 marks
2. Seven dishes in a cookery competition were each given a score out of $10$ by two judges, $X$ and $Y$. In the order of the dishes, judge $X$ gave $7,5,9,5,8,6,4$ and judge $Y$ gave $8,6,9,7,7,5,3$. The highest score is given rank $1$.
   Write down the ranks given by judge $Y$ to the seven dishes, in the order of the dishes.2 marks
3. A scientist counts the bacteria in a culture, $y$ thousand, $x$ hours after the start of an experiment. For $x=1,2,3,4,5,6,7,8$ the counts are $2,4,9,17,31,52,85,140$. Use your GDC.
   (i) Find Pearson's product-moment correlation coefficient $r$ between $x$ and $y$. (ii) Find Spearman's rank correlation coefficient $r_s$, justifying your value.3 marks