Unequal classes, frequency arrays and bivariate tables

Grouping data makes them easier to handle, but something is lost. Once values are put into the class 20-30, the table keeps only the frequency (say, 6). In calculations, all six values are treated as if they were 25, the class mark, even if they were really 21, 22, 22, 28, 29 and 29. This is called loss of information.

Unequal classes can reduce this loss. If most of the values crowd into one part of the range, those crowded classes can be split into narrower ones. Then each class mark lies closer to the actual values in its class, so it represents them better.

Some data need other kinds of table:

• A frequency array is used for a discrete variable. It lists each value with its frequency. For example, the size of households in a village: how many households have 1 member, 2 members, 3 members, and so on up to 8, with the frequencies adding up to the total number of households.
• A bivariate frequency distribution classifies two variables at once, in rows and columns. For example, a set of firms can be classified by their sales (in the rows) and their spending on advertisement (in the columns), so that each cell shows how many firms fall into both groups.

The aim is always to fit the table to the data and to the question being asked.