Coefficient of correlation

#include <iostream>
#include <vector>
#include <random>
#include <algorithm> // not necessary
#include <numeric>

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

double square_root(const double& _value)
{
    return pow(_value, 0.5);
}

double sum(const std::vector<double>& _array)
{
    return std::accumulate(_array.begin(), _array.end(), 0.0);
}

double thefuck(const std::vector<double> _x, const std::vector<double> _y)
{
    size_t n = _x.size();
    double mid_x = midvalue(_x);
    double mid_y = midvalue(_y);

    // sum is the upper part here
    double sum = 0.0;
    for (size_t i = 0; i < n; i++)
    {
        double first = _x[i] - mid_x;
        double second = _y[i] - mid_y;
        sum += first * second;
    }

    // lower part being calculated here:
    double sum_x = 0.0;
    for (size_t i = 0; i < n; i++)
    {
        double diff = _x[i] - mid_x;
        sum_x += pow(diff, 2);
    }

    double sum_y = 0.0;
    for (size_t i = 0; i < n; i++)
    {
        double diff = _y[i] - mid_y;
        sum_y += pow(diff, 2);
    }

    double lower_part = square_root(sum_x * sum_y);

    // finally:
    return sum / lower_part;
}

int main()
{
    std::vector<double> x;
    std::vector<double> y;

    for (size_t i = 0; i < 50; i++)
    {
        x.push_back((double)rand() / 100);
        y.push_back((double)rand() / 100);
    }

    std::cout << thefuck(x, y);
}