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Hello, /sci/.

I come to you today as a beggar. I need help reconciling some data in my head and I just can't seem to explain it to myself in a way that makes sense.

I'll see if greentexting can keep this succinct:

>Need weekly average of "units per hour"
>Create simple formula to calculate each day as though it was given 4 units of quarter-hour time (1 hour)
>Then average each day over a week, expecting an accurate average for the week

It was pointed out to me today, though, that the formula doesn't give accurate results when the times and "units" vary wildly from one day to the next. In my head though, I can't sort out the logic.

The formula supposes that each day receives one hour of time (4 units). Averaging each day evenly should then return the same result as the week's total units divided by the week's total time, but it doesn't. It's not even close in some cases.

I just can't wrap my head around how these numbers don't reconcile. I know I'm doing something wrong. I know the second result is accurate and the first is not; but in my head, they had ought to both be the same and I cannot figure out why they're different.

>This is for tracking some of my goals at work. It's unpaid, for my personal use only. I just like to have my numbers where I can keep an eye on them.
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>>7787544
>Averaging each day evenly should then return the same result as the week's total units divided by the week's total time, but it doesn't. It's not even close in some cases.
A weighted average would
You need to weight your mean with the time for each day.
>>
>>7787849

Right, I understand that's how to arrive at the "proper" number. What I'm having trouble with is understanding why the method above doesn't work.

It makes sense in my head like this:

>Find each day's quarter-hour average: the number of units divided by the time
>Multiply by 4, giving the number of units that would have been produced in 1 hour at that rate

Now, here, I figured the weights would shift from the time to the number of units. Producing 50 units in .25 of an hour is obviously more valuable than 50 in 1, and would be represented by the "50 in .25" becoming 200 in 1; more valuable than 50 in 1.

I figured that if you then averaged those five numbers each at 1/5th value, it should represent a fair average, but it obviously does not.

I'm just having trouble recognizing where my logic has gone wrong. I know it must be in the "units / time" function, but it makes sense in my head. It should effectively give each day an "even playing field" or a common denominator per se, allowing a basic average function to return a proper result.