Number of Items

To find the number of items, we can use the formula for the coefficient of correlation (r) and the given information about the covariance and standard deviation.

Formula:
The formula for the coefficient of correlation (r) is given by:

r = Cov(x, y) / (σx * σy)

Where:
- r is the coefficient of correlation
- Cov(x, y) is the covariance between variables x and y
- σx is the standard deviation of variable x
- σy is the standard deviation of variable y

Given Information:
- Coefficient of correlation (r) = 0.8
- Cov(x, y) = 60
- Standard deviation of y (σy) = 2.5
- Sigma x square (σx^2) = 90

Calculating Number of Items:
1. Rearrange the formula for the coefficient of correlation to solve for Cov(x, y):
Cov(x, y) = r * σx * σy

2. Substitute the given values into the formula:
Cov(x, y) = 0.8 * √(90) * 2.5
Cov(x, y) = 0.8 * 3 * 2.5
Cov(x, y) = 6

3. Now, let's use the formula for covariance to find the number of items (n):
Cov(x, y) = Σ((xi - μx) * (yi - μy)) / (n - 1)

Rearrange the formula to solve for n:
n = (Cov(x, y) * (n - 1)) / Σ((xi - μx) * (yi - μy))

4. Substitute the known values into the formula:
6 = (6 * (n - 1)) / 60

5. Solve for n by cross-multiplying and simplifying the equation:
6 * 60 = 6 * (n - 1)
360 = 6n - 6
6n = 366
n = 61

Therefore, the number of items is 61.