How to calculate average value based on duration between measurements? - sql

Question

I have data similar to this:
Price DateChanged Product
10 2012-01-01 A
12 2012-02-01 A
30 2012-03-01 A
10 2012-09-01 A
12 2013-01-01 A
110 2012-01-01 B
112 2012-02-01 B
130 2012-03-01 B
110 2012-09-01 B
112 2013-01-01 B
I want to calculate average value, but the challenge is this:
Look at the first record, price 10 is valid for a duration of one month, price 12 is valid for a duration of one month while price 30 is valid for a duration of six months.
So, a basic average for product A (10+12+30+10+12)/5 would result in 14.8 while taking duration in to account then the average price would be ~20.1.
What is the best approach to solve this?
I know I could create a sub-query with a row_number() to join against to calculate a duration, but is there a better way? SQL Server has powerful features like STDistance, so surely there is a function for this?

Answer 1

What you are looking for is called weighted average, and AFAIK, there is no built-in function in SQL Server that calculates it for you. However, is not that hard to calculate it by hand.
First, you need to find the weight of each data point, in this case, you need to find the duration of each price period. You might have some additional columns in your data that could enable easier lookup, but you could do it like this as well:
SELECT p1.Product, p1.Price, p1.DateChanged AS DateStart,
isnull(min(p2.DateChanged),getdate()) AS DateEnd
INTO #PricePlanStartEnd
FROM PricePlan p1
LEFT OUTER JOIN PricePlan p2
ON p1.DateChanged < p2.DateChanged
AND p1.Product =p2.Product
GROUP BY p1.Product, p1.Price, p1.DateChanged
ORDER BY p1.Product, p1.DateChanged
This creates a #PricePlanStartEnd temporary table that has the start and the end of each price period. I've used getdate() as the end of the current time period. If you need to just calculate an average up to the last price change, just use INNER JOIN instead of the LEFT OUTER JOIN.
After that you just need to divide the sum of (price * period) by the total length of the period, and get the answer.
Here is an SQL Fiddle with the calculation
Also when your working with months, you must remember that not all months are equal, so the price for December was active longer than it was for February.

Answer 2

Using CTE and row_number() to get monthly average up to the last dateChanged. Fiddle-Demo
;with cte as (
select product, dateChanged, price,
row_number() over (partition by product order by datechanged) rn
from x
)
select t1.product,
sum(t1.price *1.0 * datediff(month, t1.dateChanged,t2.dateChanged))/12 monthlyAvg
from cte t1 join cte t2 on t1.product = t2.product
and t1.rn +1 = t2.rn
group by t1.product
--Results
Product MonthlyAvg
A 20.166666
B 120.166666
OR if you need up to date daily average then use a LEFT JOIN Fiddle-Demo;
;with cte as (
select product, dateChanged, price,
row_number() over (partition by product order by datechanged) rn
from x
)
select t1.product,
sum(t1.price *1.0 *
datediff(day, t1.dateChanged,isnull(t2.dateChanged,getdate())))/365 dailyAvg
from cte t1 left join cte t2 on t1.product = t2.product
and t1.rn +1 = t2.rn
group by t1.product
--Results
product dailyAvg
A 21.386301
B 130.975342