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I have hourly sales data & want to aggregate it to a day level. Out of 24 hours, we are classifying 6 hrs as peak hours and 18 hrs as non-peak.

Assume peak hr sales for a day as: $X_1,X_2,\ldots,X_6$

Non-peak hr sales for a day as: $Y_1,Y_2,\ldots,Y_{18}$

How can we take a weighted average of peak hr and non-peak hrs to get the data to a day level?

Ideal case would be to use the units sold in each hour as weights. But i don't have that information. What i have instead is a supply-demand information. Out of which, the trend of hourly demand follows the trend of the hourly price.

From what I understand there are 2 ways to go about this:

  1. Use demand as weights and calculate weighted average (but demand is not equal to actual units sold)

  2. Use $$ \frac{\frac{1}{4}\sum_{i=1}^{6}X_{i} + \frac{3}{4}\sum_{i=1}^{18}Y_{i}}{15} $$ where $$ 15 = \frac{1}{4}*6 + \frac{3}{4}*18 $$

Which would be more accurate? Or is there a better way?

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Just weight the respective means by $\frac{1}{4}$ and $\frac{3}{4}$, respectively.

$$ \overline{\text{Sales}} = \frac{1}{4} \sum_{i=1}^6 X_i + \frac{3}{4} \sum_{i=1}^{18} Y_i $$

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    $\begingroup$ Thanks. This might work if we are dividing by 15. I have added more information to the question. Which method would be better in your opinion? $\endgroup$ – christinehiroki May 21 at 10:05
  • $\begingroup$ I would not divide it by 15. You want to have a daily average, obtained from two components with their respective time share. I don't see why you would divide this by 15. Plus, I don't get "(but demand is not equal to actual units sold)" means. $\endgroup$ – E. Sommer May 22 at 7:25
  • $\begingroup$ Without dividing by 15, this solution is not a weighted mean (because the weights do not sum to 1). Can you explain why you think this is appropriate? $\endgroup$ – knrumsey - Reinstate Monica May 23 at 18:16

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