If the mode and mean of a moderately asymmetrical series are 16 inches and `15*6` inches respectively, then most probable median is

Options

A. `15*73`
B. `14*60`
C. `16*02`
D. none of these

Answer

To find the most probable median given the mode and mean of a moderately asymmetrical series, we can use the relationship between these measures of central tendency. The formula we will use is:

\[ 3 \times \text{Median} = 2 \times \text{Mean} + \text{Mode} \]

### Step-by-step Solution:

1. **Identify the given values**:
- Mode = 16 inches
- Mean = 15.6 inches

2. **Substitute the values into the formula**:
\[ 3 \times \text{Median} = 2 \times 15.6 + 16 \]

3. **Calculate \(2 \times \text{Mean}\)**:
\[ 2 \times 15.6 = 31.2 \]

4. **Add the Mode to this result**:
\[ 31.2 + 16 = 47.2 \]

5. **Now, divide by 3 to find the Median**:
\[ \text{Median} = \frac{47.2}{3} = 15.7333 \text{ inches} \]

6. **Round to two decimal places** (if required):
\[ \text{Median} \approx 15.73 \text{ inches} \]

### Final Answer:
The most probable median is approximately **15.73 inches**.