Владислав Толмачев

<?php
$arr = [
	        array(
		'id'=>1,
		'number'=>5,
		'id_public'=>1
		),
		array(
		'id'=>2,
		'number'=>3,
		'id_public'=>1
		),
		array(
		'id'=>3,
		'number'=>2,
		'id_public'=>2
		),
		array(
		'id'=>4,
		'number'=>2,
		'id_public'=>4
		),
		array(
		'id'=>5,
		'number'=>1,
		'id_public'=>4
		)
	];
	
	$srch = 'number';
	$unic = 'id_public';
	
	$new_arr = [];


foreach ($arr as $value) {
    if(!isset($new_arr[$value[$unic]]))$new_arr[$value[$unic]] = [0, 0];
    $new_arr[$value[$unic]][0] += $value[$srch];//общее число
    $new_arr[$value[$unic]][1]++;//количество повторов
}

$arr = [];

foreach($new_arr as $key => $value){
	array_push($arr, array($unic=>$key, $srch=>$value[0]/$value[1]));
}

print_r($arr)




        
        ?>