# Data Scales

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Data ScalesData Scales

There are several scales of data. The scales of data from lowest to highest are: Nominal, Ordinal, Interval, Ratio.

Each data scale has certain characteristics. A data scale has the characteristics of the lower level scale, plus additional characteristics. For example, ordinal data has nominal characteristics and then some.

Nominal Data

Nominal data are data that are labels or names.

Nominal data will always be Qualitative in nature.

Examples:

* A name (of a company, or person, or type of car, etc.)

* A person's gender (Male or Female),

* Political affiliation (democrat, republican, independent, etc.)

* Marital status (single, divorced, widowed, cohabitating )

* etc.

All of the above have been examples where the data can be represented non-numerically. But what if I record the gender of students in a class numerically, using 1=M, and 2=F?

Is this still nominal data? The answer is yes.

Remember that meaningful arithmetic operations (such as computing the average value) can only be performed on QUANTITATIVE data. So, let us see if I can compute the average gender, and if the result is meaningful.

If I have a class of 50 students comprised of 20 men and 30 women, the average would be: [20(1) + 30(2)]/50 = 80/50 = 1.6 on a scale of 1=M, 2=F.

So, I can compute the average, but is it meaningful? The answer is, no - it is not meaningful to say the average gender of a student is 1.6!

This is because gender is a label, a way to categorize individuals. That label, whether represented numerically with 1 and 2, or non-numerically with M and F, still represents a label and is qualitative in nature.

Other examples of numerically-represented nominal or qualitative data are: one's telephone number, zip-code, social security number, etc.

All of these are numbers but if I average the telephone numbers of all my students, the result would not be useful or meaningful.

Ordinal Data

The next level up in data scales is ordinal data. With ordinal scale, there is order within the data and a "direction" in values. Ordinal data can be recorded as numeric or non-numeric, but it is Qualitative in nature because the difference between data values is not fixed (is not discernible).

Examples of Ordinal scales:

* Grades of Meat (Select, Choice, Premium: How much more tender or tasty is one grade than the one below it is not quantifiable).

* Grades that could be earned (A, B, C, etc.) in a class: These grades represent a "range" of points earned in class. A student who falls in that range receives the letter grade. Therefore, the difference between an A and a B or even between two A's could vary.

* Managerial level (Upper, Middle, Lower)

* Likert items on a survey

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