In a symmetric distribution, the mean, median, and mode are what relationship?

In a symmetric distribution, the mean, median, and mode are what relationship?

• A. Equal to each other
• B. Mean is smallest
• C. Median is largest
• D. Mode is smallest

Answer: (A)

In a symmetric distribution, the center is the same point for different ways of describing central tendency. The mean is the balance point, the median is the middle value when data are ordered, and the mode is the most frequent value. When the distribution is perfectly symmetric, all three descriptions point to that same center, so they are equal. A familiar example is the normal distribution, where mean, median, and mode coincide at the center. If any one of these differed, the symmetry would be violated, which is why the idea that they are all equal best captures the concept.

In a symmetric distribution, the center is the same point for different ways of describing central tendency. The mean is the balance point, the median is the middle value when data are ordered, and the mode is the most frequent value. When the distribution is perfectly symmetric, all three descriptions point to that same center, so they are equal. A familiar example is the normal distribution, where mean, median, and mode coincide at the center. If any one of these differed, the symmetry would be violated, which is why the idea that they are all equal best captures the concept.