Lagrange

Syntax: BIN\LAGRANGE x xbin xcount

If the \LAGRANGE qualifier is used, \WEIGHTS, \EDGES, \AVERAGES, and \EMPTY are not allowed.

If n = LEN(xbin), define the bin ranges, ri

r1 = xbin[1] - (xbin[2] - xbin[1])/2

ri = xbin[i] - (xbin[i] - xbin[i-1])/2  for  i = 2, 3, ..., n

rn+1 = xbin[n] + (xbin[n] - xbin[n-1])/2

For each  i = 1, 2, ..., LEN(x)  find j so that  rj ≤ x[i] < rj+1  for some  j = 1, 2, ..., n.  If  j = n, then xcount[n] is incremented by 1, otherwise, let w = (x[i]-xbin[j])/(rj+1+rj)/2 then xcount[j] is incremented by 1 - w and xcount[j+1] is incremented by w.

  Number of bins
  Average