#### Realtime Stats

```/**
* \file
* \brief Compute statistics for data entered in rreal-time
*
* This algorithm is really beneficial to compute statistics on data read in
* realtime. For example, devices reading biometrics data. The algorithm is
* simple enough to be easily implemented in an embedded system.
* \author [Krishna Vedala](https://github.com/kvedala)
*/
#include <cassert>
#include <cmath>
#include <iostream>

/**
* \namespace statistics
* \brief Statistical algorithms
*/
namespace statistics {

/**
* continuous mean and variance computance using
* first value as an approximation for the mean.
* If the first number is much far form the mean, the algorithm becomes very
* inaccurate to compute variance and standard deviation.
*/
template <typename T>
class stats_computer1 {
public:
/** Constructor
* \param[in] x new data sample
*/
void new_val(T x) {
if (n == 0)
K = x;
n++;
T tmp = x - K;
Ex += tmp;
Ex2 += static_cast<double>(tmp) * tmp;
}

/** return sample mean computed till last sample */
double mean() const { return K + Ex / n; }

/** return data variance computed till last sample */
double variance() const { return (Ex2 - (Ex * Ex) / n) / (n - 1); }

/** return sample standard deviation computed till last sample */
double std() const { return std::sqrt(this->variance()); }

/** short-hand operator to read new sample from input stream
* \n e.g.: `std::cin >> stats1;`
*/
friend std::istream &operator>>(std::istream &input,
stats_computer1 &stat) {
T val;
input >> val;
stat.new_val(val);
return input;
}

private:
unsigned int n = 0;
double Ex, Ex2;
T K;
};

/**
* continuous mean and variance computance using
* Welford's algorithm  (very accurate)
*/
template <typename T>
class stats_computer2 {
public:
/** Constructor
* \param[in] x new data sample
*/
void new_val(T x) {
n++;
double delta = x - mu;
mu += delta / n;
double delta2 = x - mu;
M += delta * delta2;
}

/** return sample mean computed till last sample */
double mean() const { return mu; }

/** return data variance computed till last sample */
double variance() const { return M / n; }

/** return sample standard deviation computed till last sample */
double std() const { return std::sqrt(this->variance()); }

/** short-hand operator to read new sample from input stream
* \n e.g.: `std::cin >> stats1;`
*/
friend std::istream &operator>>(std::istream &input,
stats_computer2 &stat) {
T val;
input >> val;
stat.new_val(val);
return input;
}

private:
unsigned int n = 0;
double mu = 0, var = 0, M = 0;
};

}  // namespace statistics

using statistics::stats_computer1;
using statistics::stats_computer2;

/** Test the algorithm implementation
* \param[in] test_data array of data to test the algorithms
*/
void test_function(const float *test_data, const int number_of_samples) {
float mean = 0.f, variance = 0.f;

stats_computer1<float> stats01;
stats_computer2<float> stats02;

for (int i = 0; i < number_of_samples; i++) {
stats01.new_val(test_data[i]);
stats02.new_val(test_data[i]);
mean += test_data[i];
}

mean /= number_of_samples;

for (int i = 0; i < number_of_samples; i++) {
float temp = test_data[i] - mean;
variance += temp * temp;
}
variance /= number_of_samples;

std::cout << "<<<<<<<< Test Function >>>>>>>>" << std::endl
<< "Expected: Mean: " << mean << "\t Variance: " << variance
<< std::endl;
std::cout << "\tMethod 1:"
<< "\tMean: " << stats01.mean()
<< "\t Variance: " << stats01.variance()
<< "\t Std: " << stats01.std() << std::endl;
std::cout << "\tMethod 2:"
<< "\tMean: " << stats02.mean()
<< "\t Variance: " << stats02.variance()
<< "\t Std: " << stats02.std() << std::endl;

assert(std::abs(stats01.mean() - mean) < 0.01);
assert(std::abs(stats02.mean() - mean) < 0.01);
assert(std::abs(stats02.variance() - variance) < 0.01);

std::cout << "(Tests passed)" << std::endl;
}

/** Main function */
int main(int argc, char **argv) {
const float test_data1[] = {3, 4, 5, -1.4, -3.6, 1.9, 1.};
test_function(test_data1, sizeof(test_data1) / sizeof(test_data1[0]));

std::cout
<< "Enter data. Any non-numeric data will terminate the data input."
<< std::endl;

stats_computer1<float> stats1;
stats_computer2<float> stats2;

while (1) {
double val;
std::cout << "Enter number: ";
std::cin >> val;

// check for failure to read input. Happens for
// non-numeric data
if (std::cin.fail())
break;

stats1.new_val(val);
stats2.new_val(val);

std::cout << "\tMethod 1:"
<< "\tMean: " << stats1.mean()
<< "\t Variance: " << stats1.variance()
<< "\t Std: " << stats1.std() << std::endl;
std::cout << "\tMethod 2:"
<< "\tMean: " << stats2.mean()
<< "\t Variance: " << stats2.variance()
<< "\t Std: " << stats2.std() << std::endl;
}

return 0;
}
```