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<HTML>
<HEAD>
<TITLE>Lagrange</TITLE>
</HEAD>
<BODY BGCOLOR="#FFFFFF" TEXT="#000000">
<P><font size="+2" color="green">Lagrange</font></P>
<TABLE border="1" cols="2" frame="box" rules="all" width="572">
<TR>
<TD width="15%" valign="top"><B>Syntax</B>:</TD>
<TD width="85%" valign="top"><CODE>
BIN\LAGRANGE x xbin xcount</CODE>
</TD></TR>
</TABLE>
<P>
If the <CODE>\LAGRANGE</CODE> qualifier is used, <CODE>\WEIGHTS, \EDGES, \AVERAGES,</CODE> and
<CODE>\EMPTY</CODE> are not allowed.</P>
<P>
If <CODE>n = <a href="../Functions/VariableCharacteristics/len.htm">LEN</a>(xbin)</CODE>, define the
bin ranges, <CODE>r<sub>i</sub></CODE></P>
<P>
<CODE>r<sub>1</sub> = xbin[1] - (xbin[2] - xbin[1])/2</CODE></P>
<P>
<CODE>r<sub>i</sub> = xbin[i] - (xbin[i] - xbin[i-1])/2</CODE> for
<CODE>i = 2, 3, ..., n</CODE></P>
<P>
<CODE>r<sub>n+1</sub> = xbin[n] + (xbin[n] - xbin[n-1])/2</CODE></P>
<P>
For each <CODE>i = 1, 2, ..., LEN(x)</CODE> find <CODE>j</CODE> so that
<CODE>r<sub>j</sub> ≤ x[i] < r<sub>j+1</sub></CODE> for some
<CODE>j = 1, 2, ..., n</CODE>. If <CODE>j = n</CODE>, then
<CODE>xcount[n]</CODE> is incremented by <CODE>1</CODE>, otherwise, let
<CODE>w = (x[i]-xbin[j])/(r<sub>j+1</sub>+r<sub>j</sub>)/2</CODE> then
<CODE>xcount[j]</CODE> is incremented by <CODE>1 - w</CODE> and <CODE>xcount[j+1]</CODE> is incremented by
<CODE>w</CODE>.</P>
<P>
<a href="nbins.htm"><img src="../shadow_left.gif">
<font size="+1" color="olive">Number of bins</font></a><br />
<a href="average.htm"><img src="../shadow_right.gif">
<font size="+1" color="olive">Average</font></a>
</P>
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