What is the relationship between the mean and standard deviation in a normal distribution?

• A. Mean equals median
• B. Mean is greater than median
• C. Standard deviation measures dispersion
• D. Both A and C are correct

Answer: (D)

In a normal distribution, the mean and median are equal, which means that the distribution is symmetric around the mean. This symmetry implies that half of the values lie below the mean/median and half lie above it. Because of this characteristic, the mean being equal to the median is a fundamental property of normal distributions.

Additionally, the standard deviation plays a critical role in understanding the spread or dispersion of the data points around the mean. It quantifies how much the individual data points vary from the mean; a smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation suggests a wider spread of values.

Therefore, both of these points are accurate in describing aspects of a normal distribution. The mean equaling the median highlights the balance point of the data, and the standard deviation provides insight into the variability of the data. Consequently, identifying both the mean being equal to the median and the standard deviation measuring dispersion as correct leads to the conclusion that the most comprehensive answer includes both components.