Mean and median of a simple distribution are 38 and 39 respectively. Then, mode will be

Options

A. 36
B. 37
C. 41
D. 40

Answer

To find the mode of a distribution when the mean and median are given, we can use the formula:

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

### Step-by-step Solution:

1. **Identify the given values**:
- Mean (M) = 38
- Median (Me) = 39

2. **Substitute the values into the formula**:
\[ 3 \times \text{Median} = \text{Mode} + 2 \times \text{Mean} \]
becomes:
\[ 3 \times 39 = \text{Mode} + 2 \times 38 \]

3. **Calculate \(3 \times 39\)**:
\[ 3 \times 39 = 117 \]

4. **Calculate \(2 \times 38\)**:
\[ 2 \times 38 = 76 \]

5. **Rearrange the equation to solve for Mode**:
\[ 117 = \text{Mode} + 76 \]
To isolate Mode, subtract 76 from both sides:
\[ \text{Mode} = 117 - 76 \]

6. **Calculate the value of Mode**:
\[ \text{Mode} = 41 \]

### Final Answer:
The mode of the distribution is **41**.