# Sum of Variance or Standard Error?

My end goal is to present the average travel time for a corridor and the standard deviation (or standard error) of that travel time. I'm not sure what to present to be statistically correct, here is the information I have to summarize:

I have the average travel time for a segment of road for a specific window of time each day of the week (say, segment A to B from 5:00 to 6:00 pm, I also have this information from B to C and C to D, etc.). I have 12 weeks of data so I basically have 60 data points for each segment (weekdays only). My first thought was to present the average and standard deviation, but then I realized I am presenting an average of averages so my standard deviation should probably be a standard error.

My problem is, in some areas I have multiple segments of road that I need to sum up and present the total average travel time (So I have 60 average travel times for A to B and 60 Average travel times for B to C, but in some areas of town I need to present the average travel time from A to C or A to D, etc.). Would it be wrong to present standard deviations of everything (including those areas of town where I am just presenting A to B), even though my data points are averages? If I am to present the standard error, and I am adding multiple segments, would my "n" just be the average of the n's in each segment? [assuming SE=SD/sqrt(n) is the correct equation to use for standard error]

This post seemed very relevant: How to 'sum' a standard deviation?, but I was worried that my situation may be different because I need to present the "A to D" information in some areas.

Hopefully I presented that clearly enough, it's a challenge to describe. Any insight will be greatly appreciated!

• It seems likely you do not have enough information. Travel times among successive segments will tend to be strongly correlated (usually positively) due to transient time-related effects such as rush hours and accidents. Those correlations are essential for computing correct assessments of the dispersion of total travel times. – whuber Aug 11 '14 at 21:42
• Not enough information or not enough data (meaning small sample size)? I do have the sample data that went in to creating those averages, but we are using Excel to process the data. We have over 30 segments to analyze and the sample size ranges from a little over 5,000 per month to around 40,000 per month with the most common probably in the 10-15k per month. So it takes some well written equations and file management to process it all. I'm more interested in doing it right than quickly, though. So I'll try to calculate the variance of each so I can present an accurate SD for the corridors. – David Aug 12 '14 at 11:32