| Vocabulary words: 6 | Slideshow version |
There are two types of data, and depending on the type, we’ll treat it differently.
Qualitative data consist of attributes, labels, or nonnumerical entries.
Quantitative data consist of numerical measurements or counts.
If you look at the average price of a Honda CRV, which at the time this data was collected was $22,795, our two pieces of data are the model and the price. The model would is qualitative, and the price quantitative.
A good starting point is words are qualitative and numbers are quantitative, but that rule can break down quickly. ID numbers, like your student ID, are technically numbers, but I don’t recommend doing any math with them since they don’t actually measure anything.
Another way to look at data is the type of measurements you can apply to them. The first we’ll look at are nominal and ordinal.
Data at the nominal level of measurement are qualitative only. Data at this level are categorized using names, labels, or qualities. No mathematical computations can be made at this level.
Data at the ordinal level of measurement are qualitative or quantitative. Data at this level can be arranged in order, or ranked, but differences between data entries are not meaningful.
Nominal we’ve seen already with car models. They act as labels and the only you can do is group, or categorize, them.
Ordinal, which sounds like ‘order’, means you can order them, but nothing else. So, think of rankings like first, second, third, etc. The difference between each rank it’s defined, just that one comes before the other.
The next two apply only to quantitative data, and bring up an interesting concept you’ve likely never thought of before.
Data at the interval level of measurement can be ordered, and meaningful differences between data entries can be calculated. At the interval level, a zero entry simply represents a position on a scale; the entry is not an inherent zero.
Data at the ratio level of measurement are similar to data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data entries can be formed so that one data entry can be meaningfully expressed as a multiple of another.
This sounds complicated, but consider the temperature 0ºC. Does that actually mean zero temperature? No heat whatsoever? No, it can obviously be colder, so that 0 landmark is just pretending to be a 0. There is still some temperature there, just not no temperature.
With something like money on the other hand, zero actually means zero. So, these two types of data behave differently, despite appearances. Because zero actually means zero, data at the ratio level means you can say things like “2 dollars is twice as much as 1 dollar”. When zero doesn’t mean zero, the statement “10ºF is twice as hot as 5ºF” doesn’t actually make any sense.
The table below is a summary of the differences between the four.
| Level of Measurement | Put data in categories | Arrange data in order | Subtract data values | Determine whether one data value is a multiple of another |
|---|---|---|---|---|
| Nominal | Yes | No | No | No |
| Ordinal | Yes | Yes | No | No |
| Interval | Yes | Yes | Yes | No |
| Ratio | Yes | Yes | Yes | Yes |