if the data are moderately non-symmetrical then which one of the following empirical relationship is correct?

Options

A. 2x Standard deviation=5x Mean deviation
B. 5x Standard deviation=2x Mean deviation
C. 4x Standard deviation=5x Meun deviation
D. 5x Standard deviation=4x Mean deviation

Answer

To solve the question regarding the empirical relationship between mean deviation (MD) and standard deviation (SD) when the data is moderately non-symmetrical, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Mean Deviation (MD) is the average of the absolute deviations from the mean.
- Standard Deviation (SD) is a measure of the amount of variation or dispersion in a set of values.

2. **Identify the Empirical Relationship**:
- The question suggests an empirical relationship between mean deviation and standard deviation for moderately non-symmetrical data.
- The specific relationship given is:
\[ MD = \frac{4}{5} \times SD \]

3. **Rearranging the Equation**:
- We can rearrange the equation to express it in another form:
\[ 5 \times MD = 4 \times SD \]
- This shows that 5 times the mean deviation equals 4 times the standard deviation.

4. **Conclusion**:
- Based on the empirical relationship, we conclude that when the data is moderately non-symmetrical, the relationship \( MD = \frac{4}{5} \times SD \) holds true.
- Therefore, the correct option is that \( MD \) is equal to \( \frac{4}{5} \) of \( SD \).

### Final Answer:
The correct empirical relationship for moderately non-symmetrical data is:
\[ MD = \frac{4}{5} \times SD \]