Question

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.

Answer 1

The correlation coefficient for the given data is approximately 0.36, indicating a moderate positive correlation between students' grades and the number of pets they have at home.

To calculate the correlation coefficient for the given data:

1. Compute Means:

Calculate the means bar{x} and bar{y} for the grade and number of pets:

`\[ \bar{x} \approx 3.36, \quad \bar{y} \approx 2.36 \]`

2. Calculate Deviations:

Find the deviations for each data point from their respective means:

Grade Deviation, Pets Deviation

3. Multiply Deviations:

Multiply the deviations for each data point:

Product of Deviations

4. Sum Products:

Sum up the products of deviations:

`\[ \text{Sum of Products} \approx 2.40 \]`

5. Calculate Standard Deviations:

Compute the standard deviations
`(\(s_x\))` and
`(\(s_y\))`:

`\[ s_x \approx 1.70, \quad s_y \approx 1.57 \]`

6. Correlation Coefficient Formula:

Apply the correlation coefficient formula:

`\[ r = \frac{\text{Sum of Products}}{(n-1) * s_x * s_y} \]`

7. Calculate r:

`\[ r = (2.40)/((11-1) * 1.70 * 1.57) \]`

`\[ r \approx 0.36 \]`

Hence, the correlation coefficient for the given data is approximately \(0.36\), indicating a moderate positive correlation between the grade and the number of pets.

Que. 3. Alfonso surveyed several students in his school. He asked them to give the grade that they are in any the number of pets they have at home. The results are shown in the table below.

Survey Results

Grade | Number of pets

5 0

6 4

2 2

1 3

4 5

2 1

4 2

1 2

4 0

3 5

5 2

Find the correlation coefficient for the data. Round to the nearest hundredth.