c++ Variance and Standard Deviation - c++

Question

I have created a program that prompts a user to enter a data set. The program stores and sorts the data, then computes a variance and the standard deviation of the array. However, I am not getting the correct computations for variance and standard deviation (the answer is slightly off). Anyone know what the issue seems to be?
#include <iostream>
#include <iomanip>
#include <array>
using namespace std;
//function declarations
void GetData(double vals[], int& valCount);
void Sort(double vals[], int& valCount);
void printSort(double vals[], int& valCount);
double Variance(double vals[], int valCount);
double StandardDev(double vals[], int valCount);
double SqRoot(double value); //use for StandardDev function
//function definitions
int main ()
{
double vals = 0;
int valCount = 0; //number of values to be processed
//ask user how many values
cout << "Enter the number of values (0 - 100) to be processed: ";
cin >> valCount;
//process and store input values
GetData(&vals, valCount);
//sort values
Sort(&vals, valCount);
//print sort
cout << "\nValues in Sorted Order: " << endl;
printSort(&vals, valCount);
//print variance
cout << "\nThe variance for the input value list is: " << Variance(&vals, valCount);
//print standard deviation
cout << "\nThe standard deviation for the input list is: " <<StandardDev(&vals, valCount)<< endl;
return 0;
}
//prompt user to get data
void GetData(double vals[], int& valCount)
{
for(int i = 0; i < valCount; i++)
{
cout << "Enter a value: ";
cin >> vals[i];
}
}
//bubble sort values
void Sort(double vals[], int& valCount)
{
for (int i=(valCount-1); i>0; i--)
for (int j=0; j<i; j++)
if (vals[j] > vals[j+1])
swap (vals[j], vals[j+1]);
}
//print sorted values
void printSort(double vals[], int& valCount)
{
for (int i=0; i < valCount; i++)
cout << vals[i] << "\n";
}
//compute variance
double Variance(double vals[], int valCount)
{
//mean
int sum = 0;
double mean = 0;
for (int i = 0; i < valCount; i++)
sum += vals[i];
mean = sum / valCount;
//variance
double squaredDifference = 0;
for (int i = 0; i < valCount; i++)
squaredDifference += (vals[i] - mean) * (vals[i] - mean);
return squaredDifference / valCount;
}
//compute standard deviation
double StandardDev(double vals[], int valCount)
{
double stDev;
stDev = SqRoot(Variance(vals, valCount));
return stDev;
}
//compute square root
double SqRoot(double value)
{
double n = 0.00001;
double s = value;
while ((s - value / s) > n)
{
s = (s + value / s) / 2;
}
return s;
}

Answer 1

There was quite a bit wrong with the code that was causing your errors. Type mismatches, but more importantly, you never created an array to store the values. You treated a plain double like an array and got lucky your program never crashed on you.
Below is a working version of your code, verified with a made up data set and Excel. I left as much of your code there as possible, just commented out when appropriate. If I commented it out, I didn't make any changes to it, so there may still be errors.
Vector over array in this case. You don't know the size up front (at compile time), and vectors are easier than dynamic arrays. You also never had an array. Vectors also know how big they are, so you don't need to pass the size around.
Type mismatches. Your functions keep expecting an array of doubles, but your sum was an int, among many other mismatches. You were also passing a plain double like it was an array, writing in memory that wasn't yours to change like that.
Best practices to start now. Stop with using namespace std;. Just qualify your names when needed, or be more specific with lines like using std::cout; at the top of a function. Your naming was all over the place. Pick a naming scheme and stick with it. Names starting with a capital letter are generally reserved for classes or types.
#include <iomanip>
#include <iostream>
// #include <array> // You never actually declared a std::array
#include <vector> // You don't know the size ahead of time, vectors are the
// right tool for that job.
// Use what's available
#include <algorithm> // std::sort()
#include <cmath> // std::sqrt()
#include <numeric> // std::accumulate()
// function declarations
// Commented out redundant functions, and changed arguments to match
void get_data(std::vector<double>& vals);
// void Sort(double vals[], int& valCount);
void print(const std::vector<double>& vals);
double variance(const std::vector<double>& vals);
double standard_dev(const std::vector<double>& vals);
// double SqRoot(double value); //use for StandardDev function
// function definitions
int main() {
int valCount = 0; // number of values to be processed
// ask user how many values
std::cout << "Enter the number of values (0 - 100) to be processed: ";
std::cin >> valCount;
std::vector<double> vals(valCount, 0);
// Was just a double, but you pass it around like it's an array. That's
// really bad. Either allocate the array on the heap, or use a vector.
// Moved to after getting the count so I could declare the vector with
// that size up front instead of reserving later; personal preference.
// process and store input values
get_data(vals);
// sort values
// Sort(&vals, valCount);
std::sort(vals.begin(), vals.end(), std::less<double>());
// The third argument can be omitted as it's the default behavior, but
// I prefer being explicit. If compiling with C++17, the <double> can
// also be omitted due to a feature called CTAD
// print sort
std::cout << "\nValues in Sorted Order: " << '\n';
print(vals);
// print variance
std::cout << "\nThe variance for the input value list is: " << variance(vals);
// print standard deviation
std::cout << "\nThe standard deviation for the input list is: "
<< standard_dev(vals) << '\n';
return 0;
}
// prompt user to get data
void get_data(std::vector<double>& vals) {
for (unsigned int i = 0; i < vals.size(); i++) {
std::cout << "Enter a value: ";
std::cin >> vals[i];
}
}
// //bubble sort values
// void Sort(double vals[], int& valCount)
// {
// for (int i=(valCount-1); i>0; i--)
// for (int j=0; j<i; j++)
// if (vals[j] > vals[j+1])
// swap (vals[j], vals[j+1]);
// }
// print sorted values
void print(const std::vector<double>& vals) {
for (auto i : vals) {
std::cout << i << ' ';
}
std::cout << '\n';
}
// compute variance
double variance(const std::vector<double>& vals) {
// was int, but your now vector is of type double
double sum = std::accumulate(vals.begin(), vals.end(), 0);
double mean = sum / static_cast<double>(vals.size());
// variance
double squaredDifference = 0;
for (unsigned int i = 0; i < vals.size(); i++)
squaredDifference += std::pow(vals[i] - mean, 2);
// Might be possible to get this with std::accumulate, but my first go didn't
// work.
return squaredDifference / static_cast<double>(vals.size());
}
// compute standard deviation
double standard_dev(const std::vector<double>& vals) {
return std::sqrt(variance(vals));
}
// //compute square root
// double SqRoot(double value)
// {
// double n = 0.00001;
// double s = value;
// while ((s - value / s) > n)
// {
// s = (s + value / s) / 2;
// }
// return s;
// }
EDIT: I did figure out the variance with an accumulator. It does require knowledge of lambdas (anonymous functions, functors). I compiled to the C++14 standard, which has been the default of major compilers for a while now.
double variance(const std::vector<double>& vals) {
auto meanOp = [valSize = vals.size()](double accumulator, double val) {
return accumulator += (val / static_cast<double>(valSize));
};
double mean = std::accumulate(vals.begin(), vals.end(), 0.0, meanOp);
auto varianceOp = [mean, valSize = vals.size()](double accumulator,
double val) {
return accumulator +=
(std::pow(val - mean, 2) / static_cast<double>(valSize));
};
return std::accumulate(vals.begin(), vals.end(), 0.0, varianceOp);
}

Answer 2

mean = sum / valCount; in Variance will be computed using integer math, then converted to a double. You need to convert to double first:
mean = double(sum) / valCount;
Your SqRoot function calculates an approximate value. You should use std::sqrt instead which will be faster and more accurate.