- #1
AllisonW4
Homework Statement
Question on worksheet: What is the random uncertainty in this set of measurements? Use the instrumental uncertainty to limit the number of digits in your random uncertainty result.
Data for dropping a pencil from a height of one meter using a stopwatch that measures to the millisecond:
0.23 s 0.28 s 0.26 s 0.26 s 0.24 s 0.26 s 0.30 s
Homework Equations
We are given that σ = (high value - low value) / (number of measurements)^1/2
(I know that this formula is a really, really rough estimation - I think the teacher is just trying to keep it a bit simpler for us instead of making us find the standard deviation)
The Attempt at a Solution
σ = (high value - low value) / (number of measurements)^1/2
σ = (0.30 s - 0.23 s) / (7)^1/2
σ = 0.02646 s
This is where I am stuck - how many digits should I round this to? I believe that the instrumental uncertainty of our stopwatch was ±0.01 s because it measured to the nearest millisecond. In the question it says to "use the instrumental uncertainty to limit the number of digits in your random uncertainty result" - should I round the uncertainty to the nearest millisecond because the watch was only accurate to the millisecond? Or do something else? Our teacher also wrote on the worksheet to "use the instrumental uncertainty to determine the last significant digit"... I am not really clear on what she means by that.