In the following question, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The mean of terms x,y and z is y, then x+z=3y.
Reason (R): Mean = `("sum of observations")/("Number of observations")`

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the problem, we need to analyze the Assertion (A) and Reason (R) provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states: "The mean of terms x, y, and z is y, then x + z = 3y."
- We need to verify if this statement is true.

2. **Using the Mean Formula**:
- The formula for the mean of three numbers (x, y, z) is given by:
\[ \text{Mean} = \frac{x + y + z}{3} \]
- According to the assertion, the mean is equal to y:
\[ y = \frac{x + y + z}{3} \]

3. **Setting Up the Equation**:
- To eliminate the fraction, we can multiply both sides of the equation by 3:
\[ 3y = x + y + z \]

4. **Rearranging the Equation**:
- Now, we can rearrange the equation to isolate x + z:
\[ x + z = 3y - y \]
- Simplifying this gives:
\[ x + z = 2y \]

5. **Conclusion**:
- The assertion states that \( x + z = 3y \), but we derived that \( x + z = 2y \). Therefore, the assertion is false.

6. **Understanding the Reason (R)**:
- The reason states: "Mean = (sum of observations) / (Number of observations)".
- This statement is true as it is the definition of the mean.

### Final Answer:
- Assertion (A) is false, and Reason (R) is true.