## Applied Mathematics## Statistics |

## What are quantitative and qualitative variables as used in statistics? |

Variables are values used to come to conclusions in a statistical study. There are two main categories: *quantitative* and *qualitative* variables. Quantitative variables can be divided into three types. Ordinal variables are measured with an ordinal scale, in which higher numbers represent higher values, even though the intervals between numbers are not necessarily equal. For example, on a five-point rating scale measuring attitudes toward cutting back on air pollution, the difference between a rating of 2 and 3 may not be the same as the difference between a rating of 4 and 5. Interval variables are measured with an interval scale, in which one unit on the scale represents the same magnitude of the characteristic being measured across the whole range of the scale. For example, the Fahrenheit scale for temperature is an interval scale, in which equal differences on this scale represent equal differences in temperature, but a temperature of 30 degrees is not twice as warm as one of 15 degrees. The third type is the ratio scale variable. It is similar to the interval scale, but with true zero points. For example, the Kelvin temperature scale is a ratio scale because it has an absolute zero. Thus, a temperature of 300 Kelvin is twice as high as a temperature of 150 Kelvin.

Qualitative variables are measured on a nominal scale, or a measurement that has assigned items to groups or categories. With these variables, there is no quantitative information and no ordering of the items is conveyed—it is qualitative rather than quantitative. Religious preference, race, and gender are all examples of nominal scales.