Calculating weighted mean for values in an array - php

Question

I have an array that contains half-hourly time periods; this array is then sub-divided into dates going back 6 weeks of 'today', each date having the amount of transactions completed on that date, in that half hour period. e.g.
[07:30:00] => Array
(
[2015-05-18] => 10
[2015-05-25] => 17
[2015-06-01] => 11
[2015-06-08] => 20
[2015-06-15] => 16
[average] => 15
)
[08:00:00] => Array
(
[2015-05-18] => 12
[2015-05-25] => 10
[2015-06-01] => 14
[2015-06-08] => 19
[2015-06-15] => 18
[average] => 15
)
This goes on for the entire business day.
The average I'm currently calculating above is a simple mean of all those values, calculated thus:
foreach($average as $half_hour => $data) {
$average[$half_hour]['average'] = round(array_sum($data)/count($data), 0, PHP_ROUND_HALF_UP);
}
What I'd like to achieve is applying more weight to the more recent dates, and lesser weight to the older values. I started off defining an array of dates I'd encounter, and setting a weight for that particular date:
$date_weights = array(
date("Y-m-d", strtotime("6 weeks ago $day")) => 0.05,
date("Y-m-d", strtotime("5 weeks ago $day")) => 0.05,
date("Y-m-d", strtotime("4 weeks ago $day")) => 0.15,
date("Y-m-d", strtotime("3 weeks ago $day")) => 0.20,
date("Y-m-d", strtotime("2 weeks ago $day")) => 0.25,
date("Y-m-d", strtotime("1 weeks ago $day")) => 0.30
);
The weights all add up to 1, which from what I understand of weighted mean calculations, keeps things simple(r). Except, this is where my poor-math brain threw an exception and refused to play any more.
I tried the following code, but that appears not to do what I'm looking for:
foreach($average as $half_hour => $data) {
// apply the desired weighting to the values
foreach($data as $date => $transactions) {
$average[$half_hour][$date] = ($date_weights[$date]*$transactions);
}
}
foreach($average as $half_hour => $data) {
$average[$half_hour]['average'] = round(array_sum($data)/count($data), 0, PHP_ROUND_HALF_UP);
}
I think I'm on the right track here ? But I'm obviously missing a step. Can any kind slightly more math-savvy person point out where I'm going wrong and how best to achieve where I'm trying to get with this? Thank you !!

Answer 1

Simply remove the division by count($data) so that you get
$average[$half_hour]['average'] = round(array_sum($data), 0, PHP_ROUND_HALF_UP);
Or pick weights that have an average of (instead of a sum) of one, and keep the division.
Also, if you have 6 weight you need to have 6 values - otherwise the weights don't add up to one. Now you seem to have 6 weights (in $date_weights but only 5 values (in $average[$half_hour], not counting average).
EDIT: If you don't want to worry about the weights adding up to one, you can use this:
$average[$half_hour]['average'] = round(array_sum($data)/array_sum($date_weights), 0, PHP_ROUND_HALF_UP);
You still have to make sure all of the weights are used, though.