What does the standard deviation measure in a normal distribution?

The standard deviation is a statistic that quantifies the amount of variation or dispersion in a set of data values. In the context of a normal distribution, it serves as a crucial measure that helps to understand how spread out the values are around the mean.

When the standard deviation is small, it indicates that the data points tend to be close to the mean, which suggests that there is less variability in the data. Conversely, a larger standard deviation signifies that the data points are spread out over a wider range of values, implying greater variability. Thus, standard deviation is central to interpreting the distribution's shape, as it helps to determine the width of the bell curve, where approximately 68% of the data falls within one standard deviation from the mean in both directions in a normal distribution.

Understanding the standard deviation allows for insights into the distribution and can inform decisions, analyses, and predictions based on the data. This makes it a vital concept in statistics, particularly when analyzing data sets that conform to a normal distribution.