Class Boundaries Definition of discrete Data

Question

why do we add and subtract 0.5 due to the definition . What is reason for this? One of the definitions can be found here: http://tistats.com/definitions/class-boundaries/ Thank you

Answer 1

Note that the claim is not that the data is discrete, but that the class labels are discrete. At your link, the answer to your question is "while preventing gaps" -- every possible value of the data ends up assigned to a class. (Sometimes you don't know that your real-world data is precisely discrete, approximately discrete, or continuous. It would be comforting to know that, regardless of which of those occurs, your process assigns a class to every possible data value.)

Say my two classes are "$1$" and "$2$" but my variable, $x$ can take any value in $[0,3]$. Suppose I make a measurement and find $x = 0.1$. Pretty clearly, this should go in the class "$1$". (I put classes in quotation marks because they are labels for ranges of values.) But what about values between $1$ and $2$? We have to put a boundary somewhere to divide values belonging to the class "$1$" and values belonging to the class "$2$". In the absence of any other reason, why not but the boundary halfway from $1$ to $2$. Then values in the interval $[0,1.5)$ are assigned to the class "$1$" and values in the interval $(1.5,3]$ are assigned to the class "$2$".

What about the value $1.5$? There are two standard ways to deal with it

• Method 1: On the one hand, the probability of a continuous variable having the value $1.5$ exactly is zero, so we need not concern ourselves with this eventuality.
• Method 2: ... Well, if that's true assign it to either class, since the probability of that choice affecting the assignment of a value is zero (by the argument used in method 1).

So just pick whichever class and attach $1.5$ to its interval.