compute time series weighted average

Question

I have a 8760x1 vector with the 1-hour average ambient temperature time series.

I want to calculate the weighted average temperature weighted by the percentage of operating hours at each temperature level.

What i thought is divide the temperature range with:

ceil(Tmax-Tmin)

and then use hist.

Are there any other suggestions? Thank you in advance.

Answer 1

mean(temperatures) should do it.

Since you have hourly measurements, the frequency of a given value will be reflecting the operating hours at that temperature level. A value that occurs frequently will therefore automatically have more weight in the average.

Answer 2

Let's say you have two vectors that are the same length, one is the temperature (temp), and the other is the amount of time at that temperature (time_at_temp). The weighted average formula is this:

wt_avg_temp = sum(temp .* time_at_temp) / sum(time_at_temp);