When is a data set said to be normally distributed?

A data set is said to be normally distributed when it exhibits a bell-shaped curve, which is a defining characteristic of a normal distribution. This shape indicates that most of the data points cluster around a central mean, with values gradually tapering off symmetrically in both directions. Specifically, in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and around 99.7% within three standard deviations.

The bell-shaped curve reflects the properties of the normal distribution, such as the mean, median, and mode being equal and located at the center. This symmetry indicates that extreme values (outliers) are equally likely to occur on either side of the mean but become increasingly rare as they move further away.

In contrast, while a data set devoid of outliers or consisting solely of positive values might exhibit certain traits associated with normal distributions, these conditions alone are not sufficient to confirm a normal distribution. The presence of at least one outlier does not automatically disqualify a set from being normal, as the overall shape of the distribution is what ultimately defines its normality.