Question

4. Alfonso surveyed several students in his school. He asked them to give the grade that they are in and the number of pets they have at home. The results are shown in the table below.

Survey Results
Grade
5
6
2
1
4
2
4
1
4
3
17
5
Number of
Pets
0
4
2
3
5
1
2
2
0
5
2
Find the correlation coefficient for the data. Round to the nearest hundredth

Answer 1

0.35

Explanation:

To find the correlation coefficient, we can use the formula:

r = (n * Σ(x * y) - Σx * Σy) / √((n * Σx^2 - (Σx)^2) * (n * Σy^2 - (Σy)^2))

where n is the number of data points, x is the grade, y is the number of pets, Σx is the sum of grades, and Σy is the sum of the number of pets.

To use this formula, we first need to find the sum of the grades and the sum of the number of pets from the data in the table.

Grade Number of Pets

5 0

6 4

2 2

1 3

4 5

2 1

4 2

1 2

4 0

3 5

17 2

sum of grades = 5+6+2+1+4+2+4+1+4+3+17+5 = 49

sum of number of pets = 0+4+2+3+5+1+2+2+0+5+2 = 26

Now we can substitute these values into the formula along with n = 12, the number of data points in the table:

r = (12 * (50 + 64 + 22 + 13 + 45 + 21 + 42 + 12 + 40 + 35 + 172 + 52) - (49*26)) / √((12 * (5^2 + 6^2 + 2^2 + 1^2 + 4^2 + 2^2 + 4^2 + 1^2 + 4^2 + 3^2 + 17^2 + 5^2) - 49^2) * (12 * (0^2 + 4^2 + 2^2 + 3^2 + 5^2 + 1^2 + 2^2 + 2^2 + 0^2 + 5^2 + 2^2) - 26^2))

Which after some calculation give us r=0.35,

So the correlation coefficient for the data is approximately 0.35.