c++ - Usage of arrays to generate random numbers

Question

I'm trying to generate N random floats between 0 and 1 where N is specified by the user. Then I need to find the mean and the variance of the generated numbers. Struggling with finding the variance.

Already tried using variables instead of an array but have changed my code to allow for arrays instead.

#include <cstdlib>
#include <ctime>
#include <cmath>
using namespace std;


int main(){
  int N, i;
  float random_numbers[i], sum, mean, variance, r;
  cout << "Enter an N value" << endl;
  cin >> N;
  sum = 0;
  variance = 0;

  for (i = 0; i < N; i++) {
    srand(i + 1);
    random_numbers[i] = ((float) rand() / float(RAND_MAX));
    sum += random_numbers[i];
    cout << random_numbers[i] << endl;
    mean= sum / N;
    variance += pow(random_numbers[i]-mean,2);

    }
  variance = variance / N;
  cout << " The sum of random numbers is " << sum << endl;
  cout << " The mean is " << mean << endl;
  cout << " The variance is " << variance << endl;

} 

The mean and sum is currently correct however the variance is not.

标签： c++

Answer 1

The mean you calculate inside the loop is a "running-mean", ie for each new incoming number you calculate the mean up to this point. For the variance however your forumla is incorrect. This:

variance += pow(random_numbers[i]-mean,2);

would be correct if mean was the final value, but as it is the running mean the result for variance is incorrect. You basically have two options. Either you use the correct formula (search for "variance single pass algorithm" or "running variance") or you first calculate the mean and then set up a second loop to calculate the variance (for this case your formula is correct).

Note that the single pass algorithm for variance is numerically not as stable as using two loops, so if you can afford it memory and performance-wise you should prefer the algorithm using two passes.

PS: there are other issues with your code, but I concentrated on your main question.