If M. D. is 12, the value of S.D. will be

Options

A. 15
B. 12
C. 24
D. none of these

Answer

To find the standard deviation (S.D.) given that the mean deviation (M.D.) is 12, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given value:**
- We know that the mean deviation (M.D.) is given as 12.
\[ \text{M.D.} = 12 \]

2. **Use the relationship between Mean Deviation and Quartile Deviation:**
- The formula relating quartile deviation (Q.D.) to mean deviation is:
\[ \text{Q.D.} = \frac{5}{6} \times \text{M.D.} \]
- Substitute the value of M.D. into the formula:
\[ \text{Q.D.} = \frac{5}{6} \times 12 \]

3. **Calculate the Quartile Deviation:**
- Perform the multiplication:
\[ \text{Q.D.} = \frac{5 \times 12}{6} = \frac{60}{6} = 10 \]

4. **Use the relationship between Quartile Deviation and Standard Deviation:**
- The formula relating standard deviation (S.D.) to quartile deviation is:
\[ \text{S.D.} = \frac{3}{2} \times \text{Q.D.} \]
- Substitute the value of Q.D. into the formula:
\[ \text{S.D.} = \frac{3}{2} \times 10 \]

5. **Calculate the Standard Deviation:**
- Perform the multiplication:
\[ \text{S.D.} = \frac{3 \times 10}{2} = \frac{30}{2} = 15 \]

6. **Final Answer:**
- Therefore, the value of the standard deviation is:
\[ \text{S.D.} = 15 \]