9.1.9  Classes: classes

The classes command groups a collection of numbers into intervals.

• classes takes two or three arguments:
  • L, a list or matrix of numbers.
  • Optionally, a and b, numbers. (By default, these will be class_min and class_size from the graphics configuration, see Section 3.5.8, which themselves default to 0 and 1.)
    or:
  • Optionally, a and M, where a is the start of the beginning interval and M consists of the midpoints of the intervals.
    or:
  • Optionally, I, a list of intervals to use.
• classes(L,a,b) returns the list [[a..a+b,n₁],[a+b..a+2b,n₂],…] where each number in L is in one of the intervals [a+kb, a+(k+1)b) and n_k is how many numbers from L are in the corresponding interval.
• classes(L,a,M) returns a similar list, but instead of [[a..a+b,n₁],[a+b..a+2b,n₂],…], the intervals are determined by a and the list of midpoints M.
• classes(L,I) returns a similar list, but instead of [[a..a+b,n₁],[a+b..a+2b,n₂],…], the intervals are given by I. In this case, not every element of L is necessarily in an interval.

Examples.

• Input:
  classes([0,0.5,1,1.5,2,2.5,3,3.5,4],0,2)
  Output:

  ⎡ ⎢ ⎢ ⎣

  0.0… 2.0 4 2.0… 4.0 4 4.0… 6.0 1

  ⎤ ⎥ ⎥ ⎦

• Input:
  classes([0,0.5,1,1.5,2,2.5,3,3.5,4],-1,2)
  Output:

  ⎡ ⎢ ⎢ ⎣

  −1.0… 1.0 2 1.0… 3.0 4 3.0… 5.0 3

  ⎤ ⎥ ⎥ ⎦

• Input:
  classes([0,0.5,1,1.5,2,2.5,3,3.5,4],1,[1,3,5])
  Output:

  ⎡ ⎢ ⎢ ⎣

  0.0… 2.0 4 2.0… 4.0 4 4.0… 6.0 1

  ⎤ ⎥ ⎥ ⎦

• Input:
  classes([0,0.5,1,1.5,2,2.5,3,3.5,4],[1..3,3..6])
  Output:

  ⎡ ⎢ ⎣

  1… 3 4 3… 6 3

  ⎤ ⎥ ⎦