In a normal distribution, which statement is true?

In a normal distribution, which statement is true?

• A. Mean equals median but not equal to mode.
• B. Median equals mode but not equal to mean.
• C. Mean equals mode but not equal to median.
• D. Mean equals median equals mode.

Answer: (D)

In a normal distribution the data are perfectly symmetric around a central value, and there’s a single peak at that center. This symmetry means the center of gravity (the mean) aligns exactly with the highest point (the mode) and the middle value that splits the data into two equal halves (the median). So the mean, median, and mode all occur at the same point. That’s why the statement that they are all equal is true. If a distribution were skewed or had multiple peaks, you’d see differences among these measures, but the normal distribution’s shape makes them coincide.

In a normal distribution the data are perfectly symmetric around a central value, and there’s a single peak at that center. This symmetry means the center of gravity (the mean) aligns exactly with the highest point (the mode) and the middle value that splits the data into two equal halves (the median). So the mean, median, and mode all occur at the same point. That’s why the statement that they are all equal is true. If a distribution were skewed or had multiple peaks, you’d see differences among these measures, but the normal distribution’s shape makes them coincide.