Relationship among dispersion measures in a normal distribution:

• $4\text{SD} = 6\text{MD} = 5\text{QD}$ has misplaced coefficients.
• For a normal distribution: $\text{QD} = \frac{2}{3}\sigma$, $\text{MD} = \sqrt{\frac{2}{\pi}}\sigma \approx \frac{4}{5}\sigma$, and $\text{SD} = \sigma$. Multiplying to obtain a common integer ratio: $\frac{\text{SD}}{15} = \frac{\text{MD}}{12} = \frac{\text{QD}}{10} \implies 4\text{SD} = 5\text{MD} = 6\text{QD}$ (since $4(15) = 5(12) = 6(10) = 60$).
• Repeating SD on both sides is incorrect.
• Inverses the relationship between SD and MD.

Option analysis:
(A) For any discrete distribution, kurtosis satisfies $\beta_2 \ge 1$, where equality is attained by a symmetric two-point distribution (e.g. $\text{Bernoulli}(0.5)$).

Effect of extreme values on averages:

• Arithmetic mean uses all numerical values directly, making it highly sensitive to extreme outliers.
• Harmonic mean is strongly influenced by extremely small values.
• Median is a positional average that depends solely on the order of observations. Changing extreme high or low values does not change the middle observation, making it robust against outliers.
• Geometric mean is affected by extreme observations.