Finding an appropriate class width and constructing class limits 

Thank you 😊

Great!

Glad it was helpful!

Typically, you would either use software to construct the histogram and distribution or use Excel to speed up the check of your choice for the width. If you could assume the data is symmetric and bell shaped, you could use Sturges’ formula. Beyond that, you would need to use trial and error, but with experience you would be able to guess a workable value in one try.

@@dmcguckian I see, thanks!

🙏 thank you!

If you have measurements that have hundredths in them, you should make the limits have hundredths too. For example, 26.00 - 28.99, 29.00 - 31.99, …

Also, you could switch to boundaries, 26 - 29, 29 - 32, 32 - 35, … but with boundaries we follow the left-end-point convention. This means the classes are treated as [26, 29) [29, 32) … so the value 29 is part of the second class not the first because left end points are in the set, not right ones. The class 26 - 29 is really 26 to 28.99999999999…

@@dmcguckian perfect! Thanks a lot!

Great!

Great!

I have videos on this topic, so you can look for the video on boundaries for help, but basically when your limits are whole numbers, the corresponding boundaries are just 0.5 below and above the limits. For example, if your class went from 20 to 29, the boundaries for that class would be 20-0.5=19.5 and 29+0.5=29.5.

Usually, going up is the best option. There are times when going up can create to much space which leaves the last class empty. That can happen if you have a large number of classes. Checking your answer is the safest option.

@@dmcguckian Thanks, this helps a lot.

I’m not sure I understand your question. There are no students in this problem, and there is no general concept of a student in this type of problem. Of course, a specific problem could have students in it, but students aren’t always a part of creating a frequency distribution. The parts of a frequency distribution are: classes and frequencies. Classes have upper limits and lower limits (or upper and lower boundaries). Frequency can be expressed in several ways and is best converted to relative frequency.

The "classes" in the context of statistics has nothing to do with students. Classes ≠ Students

It would be nice if 6 worked, because 5.1 is annoying as a class width. Unfortunately, with 18 classes using 6 leaves the last 2 classes completely empty, which means you're really only putting the data into 16 classes, not 18.

Hann

Actually, I think it is you who doesn't understand how class width works. The width is the difference between any two consecutive lower (or upper) class limits (or boundaries). You are using a width of 5 (26-21=5) class boundaries, so you think that your list includes 111. However, your upper limits cannot actually be equal to the upper limit of the next class. If that were allowed, you would not know where to put a value like 26. It is perfectly fine to use a boundary like you have attempted to do, but when using boundaries, we use the left-end-point convention. The left-end-point is inside the interval defining the class, but the right-end-point is not a part of the class. For example, 106 - 111 is actually: [106 - 111). The value 111 is not part of the set, which is a problem since 111 is our largest data value.

Masa u r wrong. Do it again its 21-25, 26-30..... But u have 26 both in the first and second class