The regression equation of x on y is `9x-2y-38=0`. If mean of x series is 6, then mean of y series is

Options

A. a) 8
B. b) 6
C. c) 10
D. d) None of these

Answer

To solve the problem, we need to find the mean of the y series (ȳ) given the regression equation of x on y and the mean of the x series (x̄).

### Step-by-Step Solution:

1. **Write the regression equation**:
The regression equation given is:
\[ 9x - 2y - 38 = 0 \]
We can rearrange this equation to express y in terms of x:
\[ 2y = 9x - 38 \]
\[ y = \frac{9}{2}x - 19 \]

2. **Substitute the mean of x (x̄)**:
We know that the mean of the x series (x̄) is 6. We will substitute x = 6 into the equation we derived for y:
\[ y = \frac{9}{2}(6) - 19 \]

3. **Calculate y**:
Now, calculate the value of y:
\[ y = \frac{9}{2} \times 6 - 19 \]
\[ y = \frac{54}{2} - 19 \]
\[ y = 27 - 19 \]
\[ y = 8 \]

4. **Conclusion**:
Since we substituted the mean of x (x̄ = 6) and found y = 8, we conclude that the mean of the y series (ȳ) is:
\[ ȳ = 8 \]

### Final Answer:
The mean of the y series is **8**.