What does it mean for data to be normally distributed?

When data is described as normally distributed, it characteristically clusters around the mean, forming a symmetric, bell-shaped curve. This means that most of the values fall within a certain range close to the mean, with fewer values appearing as you move further away from the mean in either direction. In a normal distribution, about 68% of the data lies within one standard deviation of the mean, approximately 95% within two standard deviations, and about 99.7% within three standard deviations. This property of clustering provides useful insights into the data's tendency and variability, making the normal distribution a fundamental concept in statistics.

In contrast to this correct option, a skewed distribution refers to data that is unevenly distributed, favoring one side of the mean, which does not represent the characteristics of normality. Saying that all values are equal implies a situation of no variability or diversity in the data set, which is not representative of a normal distribution. Finally, the claim that data has no central tendency would suggest a lack of a typical value around which the data clusters, which is directly opposed to the idea of a normal distribution where the mean serves as the central point around which values are organized.