In a normal distribution, which measures of central tendency are equal?

In a normal distribution, which measures of central tendency are equal?

• A. Mean, median, and mode are all equal.
• B. Mean is greater than the median.
• C. Median is greater than the mode.
• D. Mode is less than the mean.

Answer: (A)

Normal distributions are symmetric around their center, so the center value acts as the balance point, the middle value, and the most frequent value. The mean is the balance point of all observations, which sits at that center in a symmetric shape. The median is the middle value when the data are ordered, and in a symmetric distribution the halfway point aligns with the center. The mode is the peak of the curve—the most frequent value—which also lies at the center for a bell-shaped, unimodal distribution. Because the same central point serves all three roles, the mean, median, and mode are equal. When distributions are skewed, these measures can differ, with each reflecting different aspects of the distribution’s shape.

Normal distributions are symmetric around their center, so the center value acts as the balance point, the middle value, and the most frequent value. The mean is the balance point of all observations, which sits at that center in a symmetric shape. The median is the middle value when the data are ordered, and in a symmetric distribution the halfway point aligns with the center. The mode is the peak of the curve—the most frequent value—which also lies at the center for a bell-shaped, unimodal distribution. Because the same central point serves all three roles, the mean, median, and mode are equal. When distributions are skewed, these measures can differ, with each reflecting different aspects of the distribution’s shape.