Determining which methods to use to find how close a day is from the average pattern Would anyone have advice on how to determine how close a day is to matching the average pattern of all days? I would like to take each day of the year and evaluate how close that day is from the average of all days in the year.
Ultimate goal is to select 7 days in the year that are closest to this average pattern.
I think I should be looking for which day has the lowest error, but am not positive.
In this sample image, the red is the average of the year and the blue represents one day. X axis is hours, y is observation.

 A: Well if I understand correctly, you are just looking for days that closely exhibit the same movements as the average of all days. This can be accomplished by using Dynamic Time Warping. DTW returns the distance between any two series by mapping them. Check it out:
https://www.aaai.org/Papers/Workshops/1994/WS-94-03/WS94-03-031.pdf
A: You have evidently have hourly measurements, so you can devise your measure of misfit, say 
$$\sum_{h=0}^{23} | y_{ih} - \bar y_h|,$$ 
or even 
$$\sum_{h=0}^{23} (y_{ih} - \bar y_h)^2,$$ 
and choose days with values closest to 0. Here $y_{ih}$ is the value for $y$ for day $i$ and hour $h$ and $\bar y_h$ is the average over days for hour $h$. I have little interest in advocating either measure  as especially good and still less in attacking others. The point is that you need your own criterion for "close to average" that matches your concerns, and then it's just computing. 
This criterion does not explicitly focus on matching times of peaks or troughs. As just one more variation, it could be that misfit is better measured on some transformed scale, e.g. root or logarithm. 
A: IDontKnowCode's answer is good, you can definitely use DTW to compare the sets of two signals and return a distance, the lowest 7 values would be the ones that match the best. It would also be interesting to compare the cross-correlation. I expect you would have the same 7 return with the highest correlation (cross-corelation of 1 means perfectly matching, DTW distance of 0 means perfectly matching), but both use different techniques.
