What does a larger standard deviation indicate about a data set?

A larger standard deviation indicates that the values in a data set are spread out over a wider range. This means that there is a greater variability among the data points, leading to a situation where they are not tightly clustered together around the mean. Instead, the data points can be found at much higher or lower values compared to the mean, which suggests diversity in the dataset.

In contrast, a smaller standard deviation would imply that the data points are close to the mean, indicating less variability and more consistency among the observations. Understanding standard deviation is crucial in statistical analysis, as it gives insight into the distribution and spread of the data, helping to determine the reliability and predictability of results derived from the data set.