MESSAGE
| DATE | 2011-05-16 |
| FROM | Ruben Safir
|
| SUBJECT | Re: [NYLXS - HANGOUT] C++ Workshop - Notes
|
on our way to adding the standard deviation to our Distribution template
class we first created a templated function called mean, to determine
the mean value for the population of all the different values in our
chainlist::List< Distirubtion > objects
The code is as follows
/*
* =====================================================================================
*
* Filename: stats.h
*
* Description: simple distribution execise
*
* Version: 1.0
* Created: 04/15/2011 06:12:42 PM
* Revision: none
* Compiler: gcc
*
* Author: Ruben Safir,
* Company:
*
* =====================================================================================
*/
#ifndef STATS_H
#define STATS_H
#include
#include
#include
#include
#include
#include "linklist.h"
/*
* =====================================================================================
* Class: Distribution
* Description: Keeps Track of Distribution of 6's (or anything else)
* in a series of List
* =====================================================================================
*/
namespace stats{
template
class Distribution {
template friend std::ostream & operator<<(std::ostream &,
const Distribution&);
public:
/* ==================== LIFECYCLE
* ======================================= */
Distribution (T descr, int occurances = 0);
Distribution():freq(NULL),occurances(NULL){};
// Distribution ( const Distribution &other ); /* copy
// constructor */
// ~Distribution (); /*
// destructor */
/* ==================== ACCESSORS
* ======================================= */
T description()const{ return freq;}
int population()const { return occurances; }
/* ==================== MUTATORS
* ======================================= */
void increase_occ(){ ++occurances; std::cout << "description "
<< freq << " occurances " << occurances << std::endl; }
void descrease_occ(){ --occurances; }
/* ==================== OPERATORS
* ======================================= */
//Distribution& operator = ( const Distribution &other ); /*
//assignment operator */
int operator()(){
return freq;
}
bool operator==(Distribution &tmp){
if(this->freq == tmp.freq)
return true;
return false;
}
bool operator<(Distribution &tmp){
if(freq < tmp.freq)
return true;
return false;
}
chainlist::List< stats::Distribution > * tally; //a list of
distribution talleys
float stddev(chainlist::List > *);
protected:
/* ==================== DATA MEMBERS
* ======================================= */
private:
/* ==================== DATA MEMBERS
* ======================================= */
T freq; //description of how many times found in a List
int occurances; //description of how many times a frequency was
found in a list
}; /* ----- end of class Distribution ----- */
template
std::ostream & operator << ( std::ostream & os, const
Distribution & obj )
{
T desc = obj.description();
int pop = obj.population();
os << "The Identification of " << desc << " was seen " << pop ;
return os;
} /* ----- end of function operator << ----- */
template
Distribution::Distribution(T descr, int occ): occurances(occ){
freq = descr;
}
//calculation standard deviation of distribution list
//
template
float
Distribution::stddev(chainlist::List > *
tally){
float dev;
return dev;
}
/* Routine to go though a single list and add it to an existing
* distribution table */
template
void mount_individual_data_point(chainlist::List * tabulate,
chainlist::List > * table);
/* Routine to find all the occurances of a type in a list of lists */
template
void take_tally(chainlist::List
*,chainlist::List > *);
template
void take_tally(chainlist::List * tabulate,
chainlist::List > * table){
for(tabulate->cursor()=tabulate->front();tabulate->cursor() !=
tabulate->endd(); tabulate->cursor( tabulate->cursor()->next() ) ){
//build distribution list
mount_individual_data_point(tabulate, table);
}
//we are at the end of tabulate
mount_individual_data_point(tabulate, table);
table->sort(*table);
}
template
void mount_individual_data_point(chainlist::List * tabulate,
chainlist::List > * table){
int val;
stats::Distribution * j;
val = *(tabulate->cursor()->value()); //get a value
table->cursor()= table->front(); //check to see if the
distribution list exists
if(!table->cursor()){ // if not add a distribution table to the
List of distributions
j = new stats::Distribution (val);
table->insert(*j ); //now we have at least one
delete j;
j=table->cursor()->value();//and increased its population
j->increase_occ();
}else{
//otherwise search for a distribution node described as
//value
table->find_value(val);
if( table->cursor() ){
j=table->cursor()->value();//and increase its population
j->increase_occ();
}else{//otherwise add a new node
j = new stats::Distribution (val);
table->insert( *j ); //now we have one for that value
delete j;
j=table->cursor()->value();//and increased its population
j->increase_occ();
}
}
}
template
float mean_list(chainlist::List< Distribution > * tally){
if(tally->endd() == 0){
std::cout << "Empty List" << std::endl;
return;
}
int sum = 0;
tally->cursor() = tally->front();
while(tally->cursor() != tally->endd() ){
sum += tally->cursor()->value()->population() ;
tally->cursor(tally->cursor()->next());
}
sum += tally->cursor()->value()->population() ;
sum += tally->curosor->value()->population();
return sum/(tally->size());
}
}
#endif /* STATS_H */
The homework assignment for Tuesday is to finish the Standard deviation
forumula which is defined as follows
quote wikipedia:: http://en.wikipedia.org/wiki/Standard_deviation
consider a population consisting of the following eight values:
2,\ 4,\ 4,\ 4,\ 5,\ 5,\ 7,\ 9
These eight data points have the mean (average) of 5:
\frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = 5 <<===this is the return
value of stats::mean_list
To calculate the population standard deviation, first compute the
difference of each data point from the mean, and square the result of
each:
\begin{array}{lll} (2-5)^2 = (-3)^2 = 9 && (5-5)^2 = 0^2 = 0 \\
(4-5)^2 = (-1)^2 = 1 && (5-5)^2 = 0^2 = 0 \\ (4-5)^2 = (-1)^2 = 1 &&
(7-5)^2 = 2^2 = 4 \\ (4-5)^2 = (-1)^2 = 1 && (9-5)^2 = 4^2 = 16
\end{array}
Next compute the average of these values, and take the square root:
\sqrt{ \frac{(9 + 1 + 1 + 1 + 0 + 0 + 4 + 16)}{8} } = 2
This quantity is the population standard deviation; it is equal to the
square root of the variance. The formula is valid only if the eight
values we began with form the complete population. If they instead were
a random sample, drawn from some larger, “parent†population,
then we should have used 7 (which is n − 1) instead of 8 (which is
n) in the denominator of the last formula, and then the quantity thus
obtained would have been called the sample standard deviation. See the
section Estimation below for more details.
A slightly more complicated real life example, the average height for
adult men in the United States is about 70", with a standard deviation
of around 3". This means that most men (about 68%, assuming a normal
distribution) have a height within 3" of the mean (67"–73") —
one standard deviation — and almost all men (about 95%) have a
height within 6" of the mean (64"–76") — two standard
deviations. If the standard deviation were zero, then all men would be
exactly 70" tall. If the standard deviation were 20", then men would
have much more variable heights, with a typical range of about
50"–90". Three standard deviations account for 99.7% of the sample
population being studied, assuming the distribution is normal
(bell-shaped).
The code is at
http://www.nylxs.com/docs/workshops/stats.h.html
Ruben
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