Answer: To determine which statement is correct based on the given information about data sets A and B:
Data set A has a smaller standard deviation than data set B.
Data set A has a larger standard deviation than data set B.
Data set A has the same standard deviation as data set B.
The correct statement is option 1: Data set A has a smaller standard deviation than data set B.
The standard deviation is a measure of the dispersion or spread of data points around the mean. A smaller variance indicates that the data points in data set A are closer to the mean, resulting in a smaller standard deviation. Since the variance of data set A is 4 (smaller) and the variance of data set B is 8 (larger), it implies that the standard deviation of data set A is smaller than the standard deviation of data set B.
Step-by-step explanation: