In a normal distribution, how does the mean compare to the median?

In a normal distribution, the mean and the median are always equal. This characteristic is a defining property of normal distributions, which are symmetric around their mean. In such distributions, the tail on either side of the mean is a mirror image, leading to both the mean and the median being located at the center of the distribution.

The mean reflects the average value of all data points, while the median represents the middle value when data points are ordered. Because of the symmetric nature of the normal distribution, the calculation of the mean does not skew the average in one direction or another, ensuring that the median aligns with the mean.

This property of normal distributions is fundamental in statistics and is one reason why the normal distribution is often employed in various analytical contexts. In practice, when analyzing normally distributed data, one can expect both measures of central tendency to provide consistent information about the data's center.