Class width

[frailjar7]

I am doing a self-learning class in Statistics and in my book, which I've just started, it shows a definition for class width as the following:

Definition #1: "Class width for a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class from the lower (or upper) class limit of the next class."

Definition #2: But then on a following page it shows in step formation:
*Determine classes.
*Find the range: R = highest value - lowest value = H - L
in the example the higher number is: 134 and the lower number is 100

It goes on to say, "Select the number of classes desired (usually between 5 and 20). In this case, 7 is arbitrarily chosen.

Find the class width by dividing the range by the number of classes, in this case: W = R/(no. of classes) thus being: 34/7 = 4.9

Now, a few questions:

1. Is there a difference between example #1 and example #2? If so, what is it?
2. What does the "W" formula mean, if class width is clearly explained in example #1?
3. And, how do we know that 7 is arbitrarily chosen? Where did the "7" come from?

I'm terribly confused!

[Mean Joe]

I think I can make an educated guess about class width, but anyone else feel free to correct me.

1. Is there a difference between example #1 and example #2? If so, what is it?

There is no difference you need to worry about. #1 is the actual definition of class width (subtract the lower limit of one class from the lower limit of the next class). As with most (mathematical) definitions, it is very abstract. To me, it seems to be trying to even apply to cases where the classes are not "joined continuously" (I need to make my own terminology up, because I don't remember specifically learning about class width).

For example, you may be looking at frequency distribution of football players in a school (let's say school has all 12 grades). The classes may be (1st and 2nd grade), (3rd and 4th grade), (5th and 6th grade), ..., (11th and 12th grade). So the classes are not "joined continuously", because the limit for the first class (2nd grade) does not coincide with the limit for the second class (3rd grade). By definition, class width = 3 - 1 for the first class (or 4 - 2 if you subtract the upper limits). It is not class width = 2 - 1, i.e. the difference in the endpoints of the class.

In #2, it is an example. It is NOT another definition. In this example, the classes are joined continuously (like they often are). So actually you could subtract the endpoints of the class to get the class width (since the upper limit of one class "joins continuously"/coincides with the lower limit of the next class).

3. And, how do we know that 7 is arbitrarily chosen? Where did the "7" come from?

Since the range of the data was 34 (= 134 - 100), they arbitrarily chose to have 7 classes. Because 34 doesn't divide neatly (only into 1, 2, 17, or 34 classes), they picked a number that was close to dividing neatly. It's purely aesthetic.

2. What does the "W" formula mean, if class width is clearly explained in example #1?

In this example, with classes that are "joined continuously", they chose (for aesthetic reasons) to make each class have the same width, and they chose 7 classes. Since the range of the data is 34, then to make each class have the same width, you need width = 34/7. Thinking the other way, with 7 classes of equal width 34/7, they will cover a range = 7 * (34/7) = 34.

[frailjar7]

Thank you Joe! Now I don't have to dwell and worry. Thanks so much!