<?php

function median(array $elements, $offset = 0, $length = null)
{
    if ($length === null) {
        $length = count($elements)-$offset;
    }

    sort($elements);
    $half = $offset + ((int)floor(($length - 1) / 2));

    return ($elements[$half] + $elements[$half + 1 - $length % 2]) / 2;
}

function quartiles(array $elements)
{
    $length = count($elements);
    $q2 = median($elements);

    $q1 = median($elements, 0, floor($length/2));
    $q3 = median($elements, ceil($length/2));

    return [$q1, $q2, $q3];
}

function interquartile_range(array $elements, array $frequencies) {
    $set = [];
    foreach($elements as $index => $element) {
        for($i = 0; $i < $frequencies[$index]; ++$i) {
            $set[] = $element;
        }
    }

    $q = quartiles($set);

    return $q[2]-$q[0];
}

function mean(array $array)
{
    return ($n = count($array)) === 0 ? 0 : array_sum($array)/$n;
}

function standard_deviation(array $array)
{
    $n = count($array);
    $mean = mean($array);
    $carry = 0.0;

    foreach($array as $value) {
        $carry += ($value-$mean)**2;
    }

    return sqrt($carry / $n);
}