TAMU MATH140 Final Practice Exam

A higher standard deviation indicates that the values in a data set are widely spread out from the mean. Standard deviation is a measure of the amount of variation or dispersion in a set of values. When the standard deviation is large, it implies that the data points are farther away from the average, indicating high variability within the data set. In contrast, a smaller standard deviation would suggest that the data values are more closely clustered around the mean, demonstrating less variability. This means there is less diversity in the values, and they tend to be closer to the average. A high standard deviation does not imply that the mean is skewed or that the data set has no variability; in fact, it suggests the opposite—a greater range of values. Thus, when interpreting the standard deviation, a higher value reflects significant dispersion of data points from the mean.