Question

The data below are the quiz scores of 10 randomly selected statistics students and the number of hours they studied for the quiz.
Hours,x= 3, 5, 2, 8, 2, 4, 4, 5, 6, 3

Scores, y= 65, 80, 60, 88, 66, 78, 85, 90, 90, 71

Find the correlation coefficient for the given data.

Group of answer choices

0.7165

0.8465

0.0020

5.044

Answer 1

$\bar{x} = \frac{\sum x}{n} =\frac{42}{10} = 4.2\\ \bar{y} = \frac{\sum y}{n} =\frac{773}{10} = 77.3$

S.D(x) =

Σ» – )2 - Σ1 - 4.2)2 = 1.777639 n

S.D(y) =$\sqrt{\frac{1}{n}\sum (y-\bar{y})^2} = \sqrt{\frac{1}{10}\sum (y-77.3)^2} = 10.59292$

covariance(x,y) =

Στα και ) - y = 340 – 4.2 * 77.3 = 15.94 n

correlation coefficient (x,y) = $\frac{cov(x,y)}{sd(x)*sd(y)} = \frac{15.94}{1.777639*1.059292} =\frac{15.94}{18.83039} = 0.846504$

Ans = 0.8465