The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we thought the measurement was very imprecise and we only had 3 measure to do, we wanted to make the measurement the best we could, so I told them "Hey, lets measure the time it takes to make it to 2000 mm$^3$ three times and the take the simple mean of that value, so the flow rate would be $$Q^*=\dfrac{3}{t_1+t_2+t_3} \times 2000 \text{ mm}^3/s.$$ and that's it, we will minimize manipulation errors."
But someone said "that is not the best thing to do, something better is to take 3 points $(t_1,V_1), (t_2,V_2), (t_3,V_3)$, make a linear regression and use the slope as the flow rate $Q^*$
My concerns with this method is that if we take the points too separated, then some point will be near cero and therefore the error associated with the manipulation of the flask will be big, but if we take all the points near 2000, then the linear regression will be with 3 points very near each other, and if some measurement went wrong, that would affect very much the final result.
What method do you think is more precise? Why? I suppose the statistics involved are simple but I can't solve this by myself.