IB Mathematics Analysis and Approaches Question Type 1: Calculating the Pearsons Moment-correlation Coefficient r for a Bivariate Data Set Exercises

Calculate the Pearson correlation coefficient $r$ for the bivariate data set: $(1,2),(2,4),(3,6)$.

Calculate the Pearson correlation coefficient $r$ for the data: $(1,8),(2,6),(3,4),(4,2)$.

Given $n=6$, $\sum x=36$, $\sum y=52$, $\sum x^2=260$, $\sum y^2=500$, $\sum xy=270$, compute the Pearson correlation coefficient $r$.

Find the Pearson correlation coefficient for the data points $(2,1),(4,3),(6,5),(8,7),(10,9)$.

For the data $(3,14),(5,12),(7,10),(9,8),(11,6),(13,4),(15,2)$, calculate the Pearson correlation coefficient $r$.

Calculate the Pearson correlation coefficient $r$ for the data: $(1,3),(2,5),(3,7),(4,9)$.

Given that $\sum (x-5)(y-4)=50$, $\sum (x-5{)}^2=100$, $\sum (y-4{)}^2=80$, find the Pearson correlation coefficient $r$.

Given $n=5$, $\sum x=15$, $\sum y=20$, $\sum x^2=55$, $\sum y^2=98$, $\sum xy=67$, compute the Pearson correlation coefficient $r$.

The marks of 6 students in Maths ($x$) and Physics ($y$) are: $x=(45,50,55,60,65,70)$, $y=(78,82,85,88,90,93)$. Calculate the Pearson correlation coefficient $r$.

Calculate the Pearson correlation coefficient for: $x=(100,150,200,250,300)$ $y=(20,45,70,95,120)$

Consider the set of points $(1,2)$, $(2,4)$ and $(3,6)$. Define new variables $x^{\prime }=2x+3$ and $y^{\prime }=3y-4$.

Show that the Pearson correlation coefficient of $(x^{\prime },y^{\prime })$ equals that of $(x,y)$.

Calculate the Pearson correlation coefficient $r$ for the ten pairs: $(1,2),(2,4),(3,5),(4,6),(5,9),(6,10),(7,11),(8,13),(9,14),(10,15)$.