The correct answer is b) the standard deviation.
Variability refers to how spread out or dispersed a set of data points is. It helps to understand the range and distribution of data. Among the options given:
- The mode is the value that appears most frequently in a data set. While it gives information about a specific point in the data, it does not measure spread.
- The standard deviation measures the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
- The median is the middle value when the data is sorted. Like the mode, it represents a central point of the data but does not indicate how spread out the data points are.
Therefore, the standard deviation is the only measure among the options that effectively represents variability in a data set.