function variance ($a)

{

    /** variable and initializations */

    $the_variance = 0.0;

    $the_mean = 0.0;

    $the_array_sum = array_sum($a);

    $number_elements = count($a);                                                                     

    /** 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 - 1.0);

    /** return the variance */

    return $the_variance;

}