Chebyshev's Inequality to Roughly Estimate Area Under an Unknown Probability Density Curve: Reposted from www.SixSigmaPractice.multiply.com

I have always been fascinated by this generalized area under the curve theorem.
Though the estimate in itself is very weak, Chebyshev's inequality provides a very strong statistical basis for control charting.
Here is a utility that compares the actual area under the curve against to that estimated by Chebyshev's inequality.

---

The JMP JSL Script

Clear Globals();
new=EXPR(dt=open());
use_curr=expr(dt=Current Data Table());
if(is empty(Current Data Table()),new,use_curr);
bound=1.5;
j = 1;
col_list = {};
For( j = 1, j <= N Col( dt ), j++,
 col_list[j] = Column( j ) << get name
);


COMM_RUN = Expr(
 col = Column( col_name );
 modelling=col<<get modeling type;
 CONT=EXPR(
 val1 = col << get as matrix;
 counter = N Rows( val1 );
 T_counter = 0;
 mu = Mean( val1 );
 sigma = Std Dev( val1 );
 i = 1;
 For( i = 1, i <= counter, i++,
  If( val1[i, 1] <= mu + bound * sigma & val1[i, 1] >= mu - bound * sigma,
   T_counter = T_counter + 1;
   i = i + 1;
  ,
   i = i + 1
  )
 );

 Actual = T_counter / counter * 100;
 T_estimate = (1 - (1 / (bound ^ 2))) * 100;
 );
 NON_CONT=EXPR(Throw ("Data Column does not contain a continous variable data"));
 if(modelling=="Continuous",CONT,NON_CONT);
);

COMM_PRINT = Expr(
 PRINT_TEXT = "Actual area inside mean +/- " ||char(bound) || "*sigma is " || Char( round(Actual,2) ) || " while Chebyshev's inequality estimate is " || Char( round(T_estimate,2) );
 PRINT_VALUES = "Mean is equal to " ||char(round(mu,3)) || ". Sigma is equal to " ||char(round(sigma,3)) || ". The bounded interval is equal to " ||char(round(mu-bound*sigma,3)) || " to " ||char(round(mu+bound*sigma,3)) || ".";
 Print( PRINT_VALUES );
 Print( PRINT_TEXT );
);


COMM_OUTPUT = Expr(
 OUTPUT_REPORT = New Window( "Results",
  Border Box(
   Left( 10 ),
   Panel Box( "Simulation Result for " || char(col), 
    Text Box(" "),
    V LIST BOX(
     Text Box( "" ),
     Text Box( PRINT_VALUES ),
     Text Box( " " ),
     Text Box( PRINT_TEXT ),
     Text Box(" "), 
     Text Box( "sixsigmapractice.multiply.com" ) 
    ) 
   )
  )
 )
);

New Window( "Interface",
 Border Box(
  Left( 10 ),
  Panel Box( "Set values and click on RUN",
   V List Box(
    V List Box(
     H List Box(
      Text Box( "Set Bound = k" ),
      Text Box( " " ),
      combo_list = Combo Box(
       {"1.5", "2", "2.5", "3", "3.5", "4", "4.5", "5", "5.5", "6"},
       COMBO_COMM = Expr(
        k = combo_list << getselected;
        bound = Num( k );
       );
       COMBO_COMM;
      ), 

     ),
     Text Box( " " ),
     H List Box(
      Text Box( "Select Column" ),
      Text Box( " " ),
      col_select = Combo Box( col_list ),
      COL_COMM = Expr( col_name = col_select << get );
      COL_COMM;
     )
    ),
    Text Box( " " ),
    Panel Box( "Command Button",
     Button Box( "RUN ESTIMATE",
      COMBO_COMM;
      COL_COMM;
      COMM_RUN;
      COMM_PRINT;
      COMM_OUTPUT;
      OUTPUT_REPORT << reshow;
      OUTPUT_REPORT<<move window(250,50)
     )
    )
   )
  )
 )
);