Operations and statistics

Features can be defined by the allowable operations that can be performed on them. Consider two features: a person's age and their phone number. Although both these features can be described by integers, they actually represent two very different types of information. This is clear when we see which operations we can usefully perform on them. For example, calculating the average age of a group of people will give us a meaningful result; calculating the average phone number will not.

We can call the range of possible calculations that can be performed on a feature as its statistics. These statistics describe three separate aspects of data. These are—its central tendency, its dispersion, and its shape.

To calculate the central tendency of data, we usually use one or more of the following statistics: the mean (or average), the median (or the middle value in an ordered list), and the mode (or the majority of all values). The mode is the only statistic that can be applied...