Standard Deviation of a Sequence of Standard Deviations


My goal is to estimate arrival times of buses at bus stops where historical GPS data for each bus is available and real-time bus location is available for each bus. What I would like to do is use the historical data to determine the mean time (in seconds) and SD taken for a bus to travel from each stop to its next stop. No problem doing this.

Now, if the bus stops are number from 1 to N, and I know the mean time and SD for a bus to travel from stop s to stop s+1 for all s (in range 1 to N-1), then if the bus is at stop 4 I can can predict the time time needed for the bus to arrive at stop 8 by adding the mean times for the segments 4-5, 5-6, 6-7, and 7-8. My question is, how do I calculate the SD for the bus trip from stop 4 to 8 given the SD for each of the segments (4-5, 5-6, 6-7, and 7-8)?

Please keep in mind that the sample sizes used to calculate the mean time and SD from stop-to-stop will be exactly the same for every segment (stop-to-stop).

Thank you in advance for any assistance you can offer.

Last edited:


New Member
If I understand the question correctly, you want to know the standard deviation of the sum of independent variables. If so, the formula you want is :

S4..8 = sqrt (S4..5^2+S5..6^2+S6..7^2+S7..8^2)