Help with general uncertainty of measurements please!

I have been given a problem to solve based on uncertainty of measurements, however I have no idea what I am doing since I am a computer student and not a maths student (No idea why they have given me this!!!)

There is probably a really simple answer, but I am completely out of it when it comes to maths and stats..

I won't post my actual problem as I would like to work that out myself, but below is a similar problem:

**set1: Bill measures the length of 10 wires. His results are (in metres): 4.7, 4.8, 4.9, 4.9, 5.0, 5.0, 5.1, 5.1, 5.2, 5.3.**

set2: Bob measures a different batch of 10 wires and gets a mean of 5.3m and a standard deviation of 0.2m

and from this I worked out the following about set 1:

- precision = 0.1m

- mean = 5

- standard deviation = 0.1826

- accuracy = 5 +- 0.1826

- standard error = 0.0577

- 95% confidence interval = 4.887 <= x >= 5.113

- significance between both samples value using t-test = 3.323

I got given some really helpful slides by my lecturer to help me work out those above, however nothing is mentioned on uncertainty

So.... **What value of uncertainty would you estimate for the measurements?**

Any steps on how to work this out would be great!!

Also examples of how to write uncertainty would be great too!!

Thank You

Re: Help with general uncertainty of measurements please!

Two thoughts about "uncertainty" in measurements:

1. To understand the uncertainty in the operator's ability to collect the data (i.e. variability in measurement) you would measure the length of the same wire ten times, and determine the standard deviation in the measurements. But that's not the data they gave you, so that's not what they're looking for.

2. If data is reported to the nearest 0.1m, the true length could be anywhere within 0.05 meters of the reported length. Hence the total uncertainty is 0.1m. For example a wire reported as being 4.3m in length might actually be anywhere from 4.25 to 4.35 meters in length. Stated another way: two wires both reported as being 4.3m long may actually differ in length by as much as 0.1 meters. I think that's the level of uncertainty that they're looking for.

Re: Help with general uncertainty of measurements please!

Ok, I think I understand the second part.

I'll have another look at my problem.

Thanks for your help.