# Re-bucket weekly sales data and calculate descriptive statistics

I have sales data in weekly buckets like this:

weekID product SoldQty
1      1       10
2      1       20
3      1       30
4      1       40
5      1       50
6      1       60
7      1       70

1      2       10
2      2       20


Calculating the standard deviation of weekly sales per product is pretty straightforward.

Now, I am asking the question: how do you calculate the standard deviation for the same data, but bi-weekly bucketed? x-weekly bucketed?

Question 2: is there an efficient algorithm for calculating it on weekly data instead of materializing the x-weekly combinations?

From the business side it means that I have various forecast horizons (1wk, 4 wks, 6wks...) per product. And I would like to build the confidence intervals for predictions of SoldQty within the forecast horizon.

It all seems very similar to the Safety Stock calculations from logistics, but I would like to be sure.

UPDATE:

Please consider there are multiple ways to re-bucket (re-combine) this data. I think that if the new bucket contains W weeks, there are W ways to re-bucket data. For an example of 2-weekly buckets.

Way 1:

bucket wkid prod sold
1      1    1    10
1      2    1    20
2      3    1    30
2      4    1    40
3      5    1    50
3      6    1    60
4      7    1    70
...


Way 2:

bucket wkid prod sold
1      1    1    10
2      2    1    20
2      3    1    30
3      4    1    40
3      5    1    50
4      6    1    60
4      7    1    70
...


Both options make sense business-wise. Essentially you need to calculate standard deviations between sales during fortnights. And, standard deviation in way 2 should be different from way 1.

Thanks in advance for your suggestions!

## 1 Answer

If the week ID is given as you state, calculate a bucket variable $w_x=int(weekID/x)$. Then use a SQL statement to summarize the volume to levels of $w_x$.

• Hi Paul. I've discovered a nuance to this question that is not covered by your answer. Would appreciate if you had a look! Jan 23, 2017 at 8:04
• @user2516569, this can be handled with a shift $s$ in the weekID, so that $$w_x=int(\frac{weekID-s}{x})$$. The only issue this raises is that the first "bucket" might not represent a whole period, and probably would need to be discarded for the analysis.
– Paul
Jan 23, 2017 at 13:27
• Thanks a lot Paul for your contribution. Your answer is clear. An issue for me here is that you still have to "materialize" both ways of grouping in order to perform the ultimate calculation. In other words, the computational complexity is still O (a^W), W being the length of a bucket. In my case W varies from 1 to 13 which is already high. I'm looking for an algorithm or approach that makes calculating st.dev. an O(a*W) task. Constantine. Jan 24, 2017 at 15:31
• @user2516569 how is the complexity $O(a^W)$? I don't understand what you mean by "materialize." The summarization is linear with $a$.
– Paul
Jan 24, 2017 at 16:00
• Man, you're right, the summation is indeed linear. By materialising I mean that before calculating the st.dev. I need to actually create W datasets out of the initial one (and store them in memory). This is already troublesome on a large initial dataset that I have. Can you think of an algorithm with a complexity that is independent of W? Feb 6, 2017 at 15:26