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#ifndef STATS_H
#define STATS_H
#include <cmath>
//Calculates Mean and returns the result
template <class T>
double Mean ( T array[], int size ){
double sum = 0;
int i;
for ( i = 0; i < size; i++ ){
sum += (double) array[i];
}
return ( sum / size );
}
//Calculates the Population Standard Deviation and returns the result
//It is overloaded to call Mean() when not given Mean
template <class T>
double Pop_Std_Dev ( T array[], int size ){
double sum = 0, mean = Mean( array, size );
int i;
for ( i = 0; i < size; i++ ){
sum += pow( ( mean - (double)array[i] ), 2);
}
return sqrt( ( sum / size ) );
}
template <class T>
double Pop_Std_Dev ( T array[], int size, double mean ){
double sum = 0;
int i;
for ( i = 0; i < size; i++ ){
sum += pow( ( mean - (double)array[i] ), 2);
}
return sqrt( ( sum / size ) );
}
//Calculates the Standard Deviation of a Sample and returns the result
//It is overloaded to call Mean() when not given Mean
template <class T>
double Samp_Std_Dev ( T array[], int size ){
double sum = 0, mean = Mean( array, size );
int i;
for ( i = 0; i < size; i++ ){
sum += pow( ( mean - (double)array[i] ), 2);
}
return sqrt( ( sum / ( size - 1) ) );
}
template <class T>
double Samp_Std_Dev ( T array[], int size, double mean ){
double sum = 0;
int i;
for ( i = 0; i < size; i++ ){
sum += pow( ( mean - (double)array[i] ), 2);
}
return sqrt( ( sum / ( size - 1) ) );
}
//Calculates the Z Score of a value, or array of values, then returns the result(s)
//It is overloaded to call Mean(), or Pop_Std_Dev() depending on what values it is called with
//Due to the Z Score only being values with a known population mean it calls Pop_Std_Dev() instead of Samp_Std_Dev()
template <class T>
double Z_Score ( T value, double mean, double Std ){
return (double)( ( value - mean ) / Std );
}
template <class T>
double Z_Score ( T array[], int size ){
int i;
double mean = Mean( array, size ), Std = Pop_Std_Dev( array, size, mean );
double * Z_array = new double [size];
for ( i = 0; i < size; i++ )
{
Z_array[i] = ( ( array[i] - mean ) / Std );
}
return Z_array;
}
template <class T>
double Z_Score ( T array[], int size, double mean ){
int i;
double Std = Pop_Std_Dev( array, size, mean );
double * Z_array = new double [size];
for ( i = 0; i < size; i++ )
{
Z_array[i] = ( ( array[i] - mean ) / Std );
}
return Z_array;
}
template <class T>
double Z_Score ( T array[], int size, double mean, double Std ){
int i;
double * Std_array = new double [size];
for ( i = 0; i < size; i++ )
{
Std_array[i] = ( ( array[i] - mean ) / Std );
}
return Std_array;
}
//Calculates the T Score of a value, or array of values, then returns the result(s)
//It is overloaded to call Mean(), or Samp_Std_Dev() depending on what values it is called with
//Due to the T Score being values with a sample mean not population it calls Samp_Std_Dev() instead of Pop_Std_Dev()
//***Note***: Since mean and standard deviation are inputed for the first function and last they are identical to their Z_Score() companions
template <class T>
double T_Score ( T value, double mean, double Std ){
return (double)( ( value - mean ) / Std );
}
template <class T>
double T_Score ( T array[], int size ){
int i;
double mean = Mean( array, size ), Std = Samp_Std_Dev( array, size, mean );
double * Z_array = new double [size];
for ( i = 0; i < size; i++ )
{
Z_array[i] = ( ( array[i] - mean ) / Std );
}
return Z_array;
}
template <class T>
double T_Score ( T array[], int size, double mean ){
int i;
double Std = Samp_Std_Dev( array, size, mean );
double * Z_array = new double [size];
for ( i = 0; i < size; i++ )
{
Z_array[i] = ( ( array[i] - mean ) / Std );
}
return Z_array;
}
template <class T>
double T_Score ( T array[], int size, double mean, double Std ){
int i;
double * Std_array = new double [size];
for ( i = 0; i < size; i++ )
{
Std_array[i] = ( ( array[i] - mean ) / Std );
}
return Std_array;
}
#endif
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