Calculating Standard Deviation & Variance in C++

Question

So, I've posted a few times and previously my problems were pretty vague. I started C++ this week and have been doing a little project.

I'm trying to calculate standard deviation & variance. My code loads a file of 100 integers and puts them into an array, counts them, calculates the mean, sum, variance and SD. But I'm having a little trouble with the variance.

I keep getting a huge number - I have a feeling it's to do with its calculation.

My mean and sum are ok.

NB:

using namespace std;

int main() {
    int n = 0;
    int Array[100];
    float mean;
    float var, sd;
    string line;
    float numPoints;

    ifstream myfile("numbers.txt");

    if (myfile.is_open()) {
        while (!myfile.eof()) {
            getline(myfile, line);
            
            stringstream convert(line);
        
            if (!(convert >> Array[n])) {
                Array[n] = 0;
            }

            cout << Array[n] << endl;
            n++;
        }
    
        myfile.close();
        numPoints = n;
    } else
        cout << "Error loading file" << endl;

    int sum = accumulate(begin(Array), end(Array), 0, plus<int>());
    cout << "The sum of all integers: " << sum << endl;

    mean = sum / numPoints;
    cout << "The mean of all integers: " << mean << endl;

    var = (Array[n] - mean) * (Array[n] - mean) / numPoints;
    sd = sqrt(var);
    cout << "The standard deviation is: " << sd << endl;

    return 0;
}

Answer 1

Here's another approach using std::accumulate but without using pow. In addition, we can use an anonymous function to define how to calculate the variance after we calculate the mean. Note that this computes the unbiased sample variance.

#include <vector>
#include <algorithm>
#include <numeric>

template<typename T>
T variance(const std::vector<T> &vec) {
    const size_t sz = vec.size();
    if (sz == 1) {
        return 0.0;
    }

    // Calculate the mean
    const T mean = std::accumulate(vec.begin(), vec.end(), 0.0) / sz;

    // Now calculate the variance
    auto variance_func = [&mean, &sz](T accumulator, const T& val) {
        return accumulator + ((val - mean)*(val - mean) / (sz - 1));
    };

    return std::accumulate(vec.begin(), vec.end(), 0.0, variance_func);
}

A sample of how to use this function:

#include <iostream>
int main() {
    const std::vector<double> vec = {1.0, 5.0, 6.0, 3.0, 4.5};
    std::cout << variance(vec) << std::endl;
}

Answer 2

Two simple methods to calculate Standard Deviation & Variance in C++.

#include <math.h>
#include <vector>

double StandardDeviation(std::vector<double>);
double Variance(std::vector<double>);

int main()
{
     std::vector<double> samples;
     samples.push_back(2.0);
     samples.push_back(3.0);
     samples.push_back(4.0);
     samples.push_back(5.0);
     samples.push_back(6.0);
     samples.push_back(7.0);

     double std = StandardDeviation(samples);
     return 0;
}

double StandardDeviation(std::vector<double> samples)
{
     return sqrt(Variance(samples));
}

double Variance(std::vector<double> samples)
{
     int size = samples.size();

     double variance = 0;
     double t = samples[0];
     for (int i = 1; i < size; i++)
     {
          t += samples[i];
          double diff = ((i + 1) * samples[i]) - t;
          variance += (diff * diff) / ((i + 1.0) *i);
     }

     return variance / (size - 1);
}