Final answer:
The standard deviation is a statistical metric that measures the amount of variation or dispersion in a data set. It quantifies how much values deviate from the mean, indicating how spread out the data values are. When the standard deviation is low, the data values are close to the mean; when it is high, they are more spread out.
Step-by-step explanation:
The standard deviation can best be described as the measure of the overall variation in a data set. It is a number that quantifies how much the values in a data set deviate from the mean of that set. Specifically, the standard deviation is equal to the square root of the variance, which itself is the average of the squared differences between each data value and the mean.
The standard deviation can also be used to determine whether a particular data value is close to or far from the mean, providing insights into the variability of the data. A small standard deviation indicates that the data points are generally close to the mean, whereas a large standard deviation suggests that the data are more spread out. When the standard deviation is zero, it means there is no spread and all data values are equal to the mean. In the context of a probability distribution, the standard deviation measures the variability of possible outcomes of a statistical experiment.
In comparison to the options provided, the standard deviation most closely aligns with an estimate of range (plus or minus) around the expected rate of return in which the actual rate of return will tend to fall. However, this definition is not exhaustive as the standard deviation applies to any kind of data set, not just financial returns.