In a normal distribution, what represents a lower and upper limit of the data spread?

In a normal distribution, the standard deviation serves as a key measure of data spread, effectively determining the lower and upper limits of the data's dispersion from the mean. The standard deviation quantifies how much the individual data points tend to deviate from the mean, providing a clear understanding of the distribution's variability.

For a normal distribution, approximately 68% of the data points lie within one standard deviation from the mean, while about 95% are within two standard deviations, and nearly all (99.7%) fall within three standard deviations. This characteristic allows us to establish a range around the mean that captures a significant portion of the data. Thus, using standard deviation, one can delineate the intervals that encompass typical data values, giving insights into the variability and spread of the data set.

While the mean is central to the distribution, it does not indicate distance alone. Variance, while related, primarily reflects the squared deviations of data points from the mean and does not provide direct limits. Cumulative probabilities assess the likelihood of a value falling below a certain point but do not define the data spread in terms of limits. Therefore, standard deviation is the most relevant measure in describing the lower and upper boundaries of the spread in a normal distribution.