The following frequency distribution analyzes the scores on a math test. find the class boundaries of scores interval 40-59.
i already know the answer is 39.5, 59.5 but i dont understand the process. don't just comment the answer i need with *how* to get it.

  No data value can fall on a boundary. If data are integers, boundary values are halfway between integers.

Step-by-step explanation:

If the data are integers, the class boundaries are halfway between the integers you want to be in different classes.

Here, 59 is shown in the first class, and 60 is shown in the next class. The class boundary between them will be halfway between these integers, at 59.5.

Since the smallest integer in the data set is 40 or more, it is reasonable to set the boundary at 39.5. (It could be 0 or any other value less than 40.)

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The basic idea with class boundaries is that they are chosen so no data value falls on a boundary. This can sometimes be tricky if the data is essentially continuous.

If the data has a resolution of 0.001, for example, then you would set the boundary value as something plus or minus 0.0005. If you can't do that, then you define which class gets a value that falls on the boundary. You might say the class definitions are, for example, ...

It is generally easier to avoid ambiguity by defining the boundary values in such a way that no data can have a boundary value.