Which statement about dispersion is true?

Which statement about dispersion is true?

• A. When two or more distributions are plotted on a graph, the one with the most sharply peaked curve has the smallest standard deviation.
• B. The greater the dispersion around a distribution's expected value, the greater the likelihood that actual results will fall within a given range of that expected value.
• C. When a distribution is plotted on a graph, the more dispersed the distribution is, the more sharply peaked the curve is.
• D. In general, the less dispersion around the central tendency, the more risk is involved in the exposure.

Answer: (D)

Dispersion shows how spread out values are around the central value, and it connects directly to risk because wider spread means more potential deviation from the expected result. The true statement is that the distribution with the most sharply peaked curve has the smallest standard deviation. A sharp peak indicates that data are tightly clustered near the center, which corresponds to a small spread and thus a small standard deviation. In other words, less dispersion produces a more concentrated, higher peak and a lower measure of spread. The other ideas contradict this relationship: larger dispersion means data are more spread out and less likely to stay within a fixed narrow interval around the mean, so the probability within that range decreases rather than increases. A more dispersed distribution is flatter, not more sharply peaked. And generally, less dispersion means less risk since outcomes are more tightly clustered around the central value.

Dispersion shows how spread out values are around the central value, and it connects directly to risk because wider spread means more potential deviation from the expected result.

The true statement is that the distribution with the most sharply peaked curve has the smallest standard deviation. A sharp peak indicates that data are tightly clustered near the center, which corresponds to a small spread and thus a small standard deviation. In other words, less dispersion produces a more concentrated, higher peak and a lower measure of spread.

The other ideas contradict this relationship: larger dispersion means data are more spread out and less likely to stay within a fixed narrow interval around the mean, so the probability within that range decreases rather than increases. A more dispersed distribution is flatter, not more sharply peaked. And generally, less dispersion means less risk since outcomes are more tightly clustered around the central value.