A perfect Gaussian (normal) distribution occurs when which measures of central tendency are equal?

• A. Mean
• B. Mean and Median
• C. Mean, Median, and Mode
• D. Median and Mode

Answer: (C)

In a perfect Gaussian distribution, the mean, median, and mode all align at the central value μ. The normal curve is perfectly symmetric about μ and has a single peak, so the mean (the balance point), the median (the midpoint of the area), and the mode (the most probable value) all occur at the same center. That shared center is what makes all three measures equal. If the distribution were skewed or had multiple peaks, these measures could differ, but for a true Gaussian they coincide.