function standard_deviation_population ($a)
{
  //variable and initializations
  $the_standard_deviation = 0.0;
  $the_variance = 0.0;
  $the_mean = 0.0;
  $the_array_sum = array_sum($a); //sum the elements
  $number_elements = count($a); //count the number of elements

  //calculate the mean
  $the_mean = $the_array_sum / $number_elements;

  //calculate the variance
  for ($i = 0; $i < $number_elements; $i++)
  {
    //sum the array
    $the_variance = $the_variance + ($a[$i] - $the_mean) * ($a[$i] - $the_mean);
  }

  $the_variance = $the_variance / $number_elements;

  //calculate the standard deviation
  $the_standard_deviation = pow( $the_variance, 0.5);

  //return the variance
  return $the_standard_deviation;
}

<?
include ("ajstatistics.php");
$a = array(0, 1, 2, 3, 4, 5);

$standard_deviation = standard_deviation_population ($a);

echo "a[0] = $a[0]<br>";
echo "a[1] = $a[1]<br>";
echo "a[2] = $a[2]<br>";
echo "a[3] = $a[3]<br>";
echo "a[4] = $a[4]<br>";
echo "a[5] = $a[5]<br>";
echo "standard_deviation = $standard_deviation<br>";
?>