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I have salary data of 3000 employees ranging from 3000 - 10000 dollars.

Based on my understanding:(https://mathbitsnotebook.com/Algebra1/FunctionGraphs/FNGContinuousDiscrete.html)

  • Continuous data is a set of data if the values belonging to the set can take on ANY value within a finite or infinite interval.
  • Discrete data is a set of data if the values belonging to the set are distinct and separate (unconnected values).

If I apply the above definition to my data set,

  • The salary of the group can take any value within a finite or infinite interval.
  • The salary of each individual in the group is also distinct and separate.

I am new to this and quite confused here. I understand the basic difference that continuous is measured and discrete is counted.

But is the salary of the group continuous or discrete?

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    $\begingroup$ It doesn't matter. Seriously: you're better off thinking about your statistical problem instead of philosophizing over whether you should treat dollars and cents as discrete or continuous. In some contexts and some datasets, treating salary in a discrete manner could be effective (but in most contexts for most datasets for most purposes that wouldn't work very well). $\endgroup$
    – whuber
    Apr 20, 2022 at 3:55
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    $\begingroup$ Small clarification re: "discrete is counted" ... not necessarily. Count values are discrete, but the converse doesn't necessarily hold. Imagine I draw right angled triangles on the face of a die, with (base,height) as $\{(1,1), (1,2), (2,2), (1,3),(2,3),(1,4)\}$ and then I roll the die, recording as the outcome the length of the hypotenuse of the triangle that comes up on the uppermost face (which lengths are $\{√2,√5,√8,√10,√13,√17\}$ respectively). This outcome is clearly not a count -- it's not even an integer. But it is discrete, only taking 6 distinct values. $\endgroup$
    – Glen_b
    Apr 20, 2022 at 4:33

2 Answers 2

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@whuber beat me to it in the comments. It (probably) doesn't matter.

Perhaps a company only has a small set of distinct salaries covering a wide range of values, in which case you might treat them as factors in a linear model. But at many companies you will get a messier assortment of values.

In one sense you could think of salaries as discrete when you get into the details of rounding to the nearest cent, but in practice being careful about this distinction is rarely going to help you.

Just as microbiologists sometimes get away with assuming population sizes of bacterial communities are continuous, you can very likely get away with assuming continuity for salaries.

Start with your research question and figure out what you can assume with that in view.

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Go back to the definition of what is meant by a discrete and what is meant by a continuous random variable. It also helps to know that the real line is dense and asking whether it is possible that somebody gets paid a figure strictly between \$200.15 and \$200.16.

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