If `barx=0,bary=0,Sigmax_(i)y_(i)=24,sigma_(x)=3,sigma_(y)=4,andn=10`, then the coefficient of correlation is

Options

A. `0.1`
B. `0.2`
C. `0.3`
D. none of these

Answer

To find the coefficient of correlation (r) given the values:

- \( \bar{x} = 0 \)
- \( \bar{y} = 0 \)
- \( \Sigma x_i y_i = 24 \)
- \( \sigma_x = 3 \)
- \( \sigma_y = 4 \)
- \( n = 10 \)

We can follow these steps:

### Step 1: Understand the formula for the coefficient of correlation
The formula for the coefficient of correlation (r) is given by:

\[ r = \frac{\text{Cov}(X, Y)}{\sigma_X \sigma_Y} \]

Where:
- Cov(X, Y) is the covariance between X and Y
- \( \sigma_X \) is the standard deviation of X
- \( \sigma_Y \) is the standard deviation of Y

### Step 2: Calculate the covariance
Since both \( \bar{x} \) and \( \bar{y} \) are 0, the covariance can be simplified as:

\[ \text{Cov}(X, Y) = \frac{\Sigma (x_i - \bar{x})(y_i - \bar{y})}{n} = \frac{\Sigma x_i y_i}{n} \]

Substituting the known values:

\[ \text{Cov}(X, Y) = \frac{24}{10} = 2.4 \]

### Step 3: Substitute the values into the correlation formula
Now, we can substitute the covariance and the standard deviations into the correlation formula:

\[ r = \frac{2.4}{3 \times 4} \]

### Step 4: Calculate the denominator
Calculate the denominator:

\[ 3 \times 4 = 12 \]

### Step 5: Calculate the correlation coefficient
Now substitute back into the formula:

\[ r = \frac{2.4}{12} = 0.2 \]

### Conclusion
Thus, the coefficient of correlation \( r \) is:

\[ \boxed{0.2} \]