A qualitative variable is normally described in words rather than numerically. A quantitative variable assumes meaningful numerical values, and can be further categorized as either discrete or continuous. A discrete variable assumes a countable number of distinct values, whereas a continuous variable can take on any value within an interval.

All data measurements can be classified into one of four major categories.

• The nominal scale represents the least sophisticated level of measurement. The values in nominal data differ merely by name or label, and the values are then simply categorized or grouped by name.

• The values of data on an ordinal scale can be categorized and ranked; however, differences between the ranked values are meaningless.

• The interval scale is a stronger measurement scale as compared to nominal and ordinal scales. Values on the interval scale can be categorized and ranked, and differences between scale values are valid. The main drawback of the interval scale is that the value of zero is arbitrarily chosen; this implies that ratios constructed from interval-scaled values bear no significance.

• The ratio scale represents the strongest level of measurement. Ratio-scaled data have all the characteristics of interval-scaled data as well as a true zero point as the origin; thus, as its name implies, meaningful ratios can be calculated with values on the ratio scale.

Nominal and ordinal scales are used for qualitative variables. Values corresponding to qualitative data are typically expressed in words but are coded into numbers later on for purposes of data processing. When summarizing the results of qualitative data, we typically count the number or calculate the percentage of persons or objects that fall into each possible category. Interval and ratio scales are used for quantitative variables.

Unlike qualitative variables, arithmetic operations are valid on quantitative variables. P-7