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Class Widths confusion
By Hal 2001 (P3046) on Monday, October 16, 2000 - 08:10 pm:

Hi,

Confusion over class widths:
If you have the following data:

Mass (lb) 0-19 20-29 30-39 40-49
No. of students 16 26 36 22

Class widths (0 to 20) = 20, (20 to 30) = 10, (30 to 40) = 10, (40-50) = 10
or should the class widths be : (-0.5 to 19.5) etc etc??
Freq Density 16/20=0.8, 26/10=2.6, 36/10=3.6, 22/10=2.2
(Freq/Class width)

Q: If I had to draw a Histogram, plotting variate against Frequency density,
what would be the 'class width' for each of the classes in the above data be?
I need the class widths so that the Frequeny Density can be worked out by (freq/class width).
Do my class widths look alright?

What would the class widths be in the following?
  1. Milage (000 miles) 1-12, 13-16, 17-20, 21-25 (mileage covered was rounded to the nearest 1000 miles)
  2. Marks <=20, <=30, <= 40, <=60, <=100
  3. Time (sec) 240-259, 260-269, 270-274, 275-290 (nearest second)
  4. x 1-5, 6-10, 11-15, 16-20, 21-25, 26-30, 31-35, 36-40 (nearest whole number)
  5. Time (sec) -20, -40, -50, -60, -80, -100, -120
I am not always sure of what are the general rules when it comes to deciding on the class widths, in particular dealing with Histograms and other averages. Can anyone help out in clearing this up for me with a few good varying examples?

Regards
HAL2001
By Michael Ching (Mcc32) on Saturday, October 21, 2000 - 07:27 pm:

The point of a histogram is to group data points together into categories that allow you to observe important features of the data without worrying about the precise values.

In determining class widths you have to think about what values of the data fall into what categories. There are two main cases:

  1. Continuous data (eg mass, time)

    Here the data points can take any of a continuous range of values. When the data is reported we normally have to round it to make it easier to handle. This must be taken into account when thinking about the class widths. So, in the first example you give about the masses of students we have to think about which values would be put into the category 0-19 lb. Now, since masses cannot be negative the lower bound for this must be 0. Assuming that the masses have been rounded to whole numbers before being put into the given categories, the largest value that would have fallen into the 0-19 category would be 19.49999... (19.5 would have been rounded to 20 and gone in the next category up). So the actual class width for this category is 0-19.5 (although the actual value 19.5 would go in a different category, anything smaller - e.g. 19.499999999999999999999999999999999999999999999999999 - would be OK so 19.5 is the boundary of the category 0-19). If we work out the width of this class we get 19.5 - 0 = 19.5 which unfortunately isn't a nice round number. I'm afraid that's life! We have to think about the same things for the next category up - that is, 20-29 lb. The lower bound here is 19.5 and the upper is 29.5. Here the width of the class is 29.5 - 19.5 = 10. Similarly for the others.

  2. Discrete (e.g. number of people at a football match, shoe size)

    Here the data can only take certain values - usually whole numbers (or halves in the case of shoe size). The way to work out class sizes for this sort of data is as follows. Suppose we have a class 1-2 people. We have to think how many different numbers would fall into this class. Well, a number 1 would go in and so would a number 2. Therefore there are 2 different numbers and the class width (although here it would make more sense to call it a class size) is 2. If our next class was 3-5 then the different possible numbers are 3, 4 and 5 so the class size is 3. Note that this is different to what you would get by simply subtracting the start and endpoints of the classes.
Therefore for each set of data for which you need to work out the class widths the first thing to do is to decide if it is continuous or discrete. Then you either apply the idea in section 1 or section 2 to get the answer.
By Hal 2001 (P3046) on Sunday, October 22, 2000 - 08:04 pm:

Hi Michael,

Thank you for your post.
It clears up a lot of my thoughts on classes.

Thanks once again!
HAL2001