Covariance (x,y) between x and if `sumx=15, sum y=40, sumxy=110, n=5` is

Options

A. 22
B. `-2`
C. 2
D. None of these

Answer

To find the covariance between two variables \( x \) and \( y \) given the following values:

- \( \text{sum}x = 15 \)
- \( \text{sum}y = 40 \)
- \( \text{sum}xy = 110 \)
- \( n = 5 \)

We will use the formula for covariance:

\[ \text{Cov}(x, y) = \frac{\sum xy - \frac{\sum x \cdot \sum y}{n}}{n} \]

### Step-by-Step Solution:

1. **Calculate the means of \( x \) and \( y \)**:
- Mean of \( x \) (\( \bar{x} \)):
\[ \bar{x} = \frac{\text{sum}x}{n} = \frac{15}{5} = 3 \]
- Mean of \( y \) (\( \bar{y} \)):
\[ \bar{y} = \frac{\text{sum}y}{n} = \frac{40}{5} = 8 \]

2. **Substitute the values into the covariance formula**:
- We need to calculate \( \sum xy \) and \( \frac{\sum x \cdot \sum y}{n} \):
\[ \sum xy = 110 \]
\[ \frac{\sum x \cdot \sum y}{n} = \frac{15 \cdot 40}{5} = \frac{600}{5} = 120 \]

3. **Calculate the covariance**:
- Now substitute these values into the covariance formula:
\[ \text{Cov}(x, y) = \frac{110 - 120}{5} = \frac{-10}{5} = -2 \]

Thus, the covariance \( \text{Cov}(x, y) \) is \(-2\).

### Final Answer:
\[ \text{Cov}(x, y) = -2 \]