If quartile deviation of a sample is 20, then the most likely value of SD is

Options

A. 30
B. 12
C. 18
D. 13

Answer

To find the standard deviation (SD) given the quartile deviation (QD), we can use the relationship between these two measures of dispersion. The formula we will use is:

\[ SD = \frac{3}{2} \times QD \]

### Step-by-Step Solution:

1. **Identify the given value**:
We are given that the quartile deviation (QD) is 20.

2. **Substitute the value into the formula**:
Using the formula for standard deviation, we substitute QD with 20:
\[ SD = \frac{3}{2} \times 20 \]

3. **Calculate the multiplication**:
First, calculate \( \frac{3}{2} \times 20 \):
\[ SD = \frac{3 \times 20}{2} = \frac{60}{2} = 30 \]

4. **Conclusion**:
The most likely value of the standard deviation (SD) is 30.

### Final Answer:
The most likely value of the standard deviation is **30**.

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