Charlier's Check

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/CharliersCheck.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CharliersCheck.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Example

c=10;
x0=74.5;
x=Range[34.5,94.5,c];
xbar=Plus@@x/Length[x];
f={2,3,11,20,32,25,7};
u=(#-x0)/10&/@x;
ubar=Tr[u]/Length[u];
t={
Append[x,""],
Append[f,Tr[f]],
Append[u,""],
Append[Times[f,u],Tr[Times[f,u]]],
Append[Times[f,u^2],Tr[Times[f,u^2]]],
Append[Times[f,(u+1)^2],Tr[Times[f,(u+1)^2]]]
};

DisplayForm[GridBox[Transpose@t,GridFrame->True,RowLines->True,ColumnLines->True,ColumnAlignments->Right]]

176.+2(-20.)+100

{Sum[f[[i]](x[[i]]-xbar)^2,{i,Length[f]}]/c^2,Sum[f[[i]](u[[i]]-ubar)^2,{i,Length[f]}]}

f.u/Tr[f]

176/100-(-20./100)^2

Sqrt[172.]