Calculating average of fluctuations from a data set

Question

I have a given data set, 4500 time data points approx, and the instantaneous velocity at each point. To calculate the time average of the velocity, I attempted to integrate the velocity function numerically wrt each time step using the trapezoid method. Once I added up each segment $$\sum_{i=1}^{4500} \frac{v(t_{i+1})+v(t_i)}{2}*(t_{i+1} - t_i)$$ I multiplied by $1/(T_{4500}-T_{1})$, and calculated at each step the fluctuation: $$u_i' = \bar{u} + u_i$$ I am a bit unsure on how to take the average of the fluctuation terms, if I take the sum and divide it by the total number of points (4500) I get 0.031 (a term close to zero); on the other hand, if I divide the sum by the the time interval $T_{4500}-T_{1}$ I get a value of 2. The second value confuses me as I expect the average of the fluctuations to be zero, should I only consider the point avg rather than the time average of the fluctuations?