How to Calculate the sample mean, standard deviation, and variance in C++ from random distributed data and compare with original mean and sigma

There is no standard deviation function C++, so you’d need to do write all the necessary functions yourself — Generate random numbers and calculate the standard deviation.

double stDev(const vector<double>& data) {
    double mean = std::accumulate(data.begin(), data.end(), 0.0) / data.size();
    double sqSum = std::inner_product(data.begin(), data.end(), data.begin(), 0.0);
    return std::sqrt(sqSum / data.size() - mean * mean);
}

int main() {

    double x_mu = 25;
    double x_sigma = 5;
    size_t size = 1000;
    std::normal_distribution<double> x_distribution(x_mu, x_sigma);

    //generate random numbers and store them in a vector
    vector<double> data(size);
    std::random_device rd;
    std::mt19937 gen(rd());
    for(size_t i=0; i<size; i++) {
        data[i] = x_distribution(gen);
    }

    double test_distribution = stDev(data); 
    cout << test_distribution << endl;
    return 0;
}

Update:
To get mean, variance and standard deviation, you may create separate functions to do the calculations. One possible implementation would be:

double mean(const vector<double>& data) {
        return  std::accumulate(data.begin(), data.end(), 0.0) / data.size();
}

double variance(const vector<double>& data) {
        double xBar = mean(data);
        double sqSum = std::inner_product(data.begin(), data.end(), data.begin(), 0.0);
        return sqSum / data.size() - xBar * xBar;
}

double stDev(const vector<double>& data) {
     return std::sqrt(variance(data));       
}