In the following question, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If the median and mode of a frequency distribution are 150 and 154 respectively. Then its mean is 148.
Reason (R): Mean, median and mode of a frequency distribution are related as 3Mean=3Median - Mode.

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 given assertion and reason statements regarding the relationship between mean, median, and mode in a frequency distribution.

### Step-by-Step Solution:

1. **Understand the Assertion (A)**:
- The assertion states that if the median is 150 and the mode is 154, then the mean is 148.

2. **Understand the Reason (R)**:
- The reason states that the relationship between mean, median, and mode is given by the formula:
\[ 3 \times \text{Mean} = 3 \times \text{Median} - \text{Mode} \]

3. **Check the Given Formula**:
- The correct relationship is:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
- However, the reason provided in the question is incorrect.

4. **Use the Correct Formula**:
- Rearranging the correct formula gives us:
\[ 2 \times \text{Mean} = 3 \times \text{Median} - \text{Mode} \]
- This can be rewritten as:
\[ \text{Mean} = \frac{3 \times \text{Median} - \text{Mode}}{2} \]

5. **Substitute the Values**:
- Substitute the given values of median and mode into the formula:
- Median = 150
- Mode = 154
- Plugging in these values:
\[ \text{Mean} = \frac{3 \times 150 - 154}{2} \]

6. **Calculate the Mean**:
- Calculate \(3 \times 150\):
\[ 3 \times 150 = 450 \]
- Now substitute this back into the equation:
\[ \text{Mean} = \frac{450 - 154}{2} \]
- Calculate \(450 - 154\):
\[ 450 - 154 = 296 \]
- Now divide by 2:
\[ \text{Mean} = \frac{296}{2} = 148 \]

7. **Conclusion**:
- The calculated mean is indeed 148, which confirms the assertion is correct.
- However, the reason provided is incorrect because the formula stated is not the standard relationship between mean, median, and mode.

### Final Answer:
- The assertion (A) is true, and the reason (R) is false. Therefore, the correct choice is that the assertion is correct, but the reason is incorrect.