Question

Classifying individuals into low, middle, and high categories implies a scale of which type?

Answer 1

Answer:

There are two meanings of Likert scales. It is either a single item with a number of discrete values, such as five, or it is several items which are combined together into a single variable. I suspect you are talking about the former.

That being the case you have ordinal data which means that you should not be calculating a mean and a standard deviation as these forms of summary statistic are only permissible with scale data. The kinds of summary statistic you are permitted to calculate are minimum, maximum, median, quartiles, range and interquartile range.

If subsequently you wish to classify a data series as low, medium or high then you need to define how you wish to this this, e.g. by on the basis of the median.