Question

The scores of the quizzes of five students in both English and Science are:

English Science

Student 1 6 8

Student 2 5 5

Student 3 9 6

Student 4 4 7

Student 5 8 9

For English, the mean is 6.4 and the standard deviation is 2.0. For Science, the mean is 7 and the standard deviation is 1.6. Using the formula below or Excel, find the correlation coefficient, r, for this set of scores. Answer choices are rounded to the nearest hundredth. ram-izlet 0

a) 0.23

b) 0.05

c) 0.50

d) 0.42

Answer 1

0.23

Explanation:

Given the data:

____(x) __(y)__(x - m1) /s1 ___(y-m2) /s2

1 ___6 ___8__ - 0.2 _______0.625

2 __5 ___ 5__ - 0.7________ - 1.25

3 __9____6__ 1.3 ________ - 0.625

4__ 4____ 7__ - 1.2 ______ 0

5__ 8 ____9 _ 0.8 _______ 1.25

For English :

Mean score(m1) = 6.4

Standard deviation (s1) = 2.0

For Science :

Mean score (m2) = 7.0

Standard deviation (s2) = 1.6

n = number of observations = 5

Correlation Coefficient (r) :

r = 1/(n - 1) Σ[((X - m1) / s1) * ((Y - m2) /s2)]

(-0. 2 * 0.625) + (-0.7 * - 1.25) + (1.3 * - 0.625) + (-1.2 * 0) + (0.8 * 1.25) = 0.9375

r = 0.9375/(5-1)

= 0.234

= 0.23