How to work out the uncertainty of some measurements?

[a66as]

Homework Statement

i am trying to work out the uncertainty of some measurements but i don't know how to, i tried finding some info on it online but i cant, well these are my 10 measurements

9.13mm
9.12mm
9.13mm
9.12mm
9.12mm
9.13mm
9.13mm
9.12mm
9.13mm
9.12mm

Homework Equations

The Attempt at a Solution

i have worked out that the average is 9.125 but i don't have a clue on how to work out the uncertainty, any help would be appreciated, you don't have to give an answer just tell me what you can to calculate to work it out

 

[2ltben]

The uncertainty is the standard deviation. Subtract each value from the mean, square that result, add them together, divide by n-1 (9 in this case), and take the square root of that.

It's generally represented by a plus-or-minus sign, but that doesn't mean that the average falls between the range created by that value, that's a different calculation involving confidence intervals.

 

[dlgoff]

When you use an instrument to make measurements, your uncertainty depends on its accuracy.

When it is inaccurate, the uncertainty is larger than the standard deviation of the repeated measures.

http://en.wikipedia.org/wiki/Measurement_uncertainty"

 

[a66as]

after doing some research online i found this formula



Random Uncertainty = Maximum reading - Minimum reading
-----------------------------------
Number of readings

so if i did 9.13 - 9.12 and divided it by 10 i would get the answer 1x10 to the power of -3

0.01 is this the correct answer?

 

[andrewm]

Typically, scientists use the standard deviation of a set of measurements to quantify the uncertainty. To give a meaningful uncertainty in practice, however, a scientist should also include device precision and reading error.

 

[fluidistic]

When you use an instrument to make measurements, your uncertainty depends on its accuracy.

http://en.wikipedia.org/wiki/Measurement_uncertainty"

Exactly. If you get by some formula that the uncertainty is smaller than the accuracy of your instrument then the uncertainty is simply the accuracy of your instrument.
Using

The uncertainty is the standard deviation. Subtract each value from the mean, square that result, add them together, divide by n-1 (9 in this case), and take the square root of that.

you can get a very small uncertainty if you have a lot of values. Say you measured a building with a meter rule and you get an uncertainty of 1 nanometer you realize it's meaningless to say the uncertainty is smaller than the accuracy of your instrument.

 

[naresh]

after doing some research online i found this formula



Random Uncertainty = Maximum reading - Minimum reading
-----------------------------------
Number of readings

so if i did 9.13 - 9.12 and divided it by 10 i would get the answer 1x10 to the power of -3

0.01 is this the correct answer?

Note the term "random uncertainty". This refers, therefore, to multiple measurements where the data and/or the measurement changed because of randomness. This assumes that your measurement is infinitely accurate, as others have pointed out. Your measurements have only two significant digits after the decimal point, therefore an uncertainty of 0.001 does not really make sense. It would help to know what your measurements are of and how the measurements were done.

Assuming the measurement is perfect (a theoretical measurement ) and a large number of measurements, a standard deviation as mentioned by 2ltben is a better measure of the random uncertainty than the formula you have.