• Relationship Between Dispersion Measures in Normal Distribution:
• For a perfectly normal distribution $X \sim \text{N}(\mu, \sigma^2)$:
• Standard Deviation (SD): $\text{SD} = \sigma$
• Mean Deviation (MD) about mean: $\text{MD} = \sqrt{\frac{2}{\pi}} \sigma \approx 0.7979 \sigma \approx \frac{4}{5}\sigma$
• Quartile Deviation (QD) (Semi-interquartile range): $\text{QD} = 0.6745 \sigma \approx \frac{2}{3}\sigma$
• Deriving the Proportional Ratio:

$$\text{QD} : \text{MD} : \text{SD} = \frac{2}{3}\sigma : \frac{4}{5}\sigma : \sigma$$

• Multiplying throughout by the common denominator 15:

$$\left(\frac{2}{3} \times 15\right) : \left(\frac{4}{5} \times 15\right) : (1 \times 15) = 10 : 12 : 15$$

• Conclusion: The relationship that holds good is 10 : 12 : 15 (Option 1).

Correct option: (1) 10:12:15