How do you find absolute error, when finding an average of quantities?

Question

How do you find absolute error, when finding an average of quantities?
Hi, this is an important question, but there are no answers on it that don't involve complex statistics info..i am doing mechanics and not statistics for maths, so if anyone could help please do :)

When u are given say 3 quantities and their errors
A +- 0.1 B +- 0.2 C +- 0.3

if you had to find the average of the 3 quantities..
then how do you find the absolute error after that?
Please explain with a bit of detail ..thank you!

Answer 1

A common approach to this sort of problem is to use the statistical standard deviation as a measure of data spread.



This approach assumes that the errors are a random spread.



The mean of the data is given by: -



x(mean) = x1 + x2 + x3 + ... + xn

................._____________________

...........................n



Where each of the x's are measured data points for the n recorded measurements.



The standard deviation σ is given by: -



σ = √(∑(xi - x(mean))/(n-1))



Where ∑ means the sum of and the xi's are the individual data points.



However, with systematic errors e1, e2, ... en (those errors due to calculations or measuring procedures). The resultant error E is given by: -



E = √(e1² + e2² + e3² + ... + en²)



This resultant error may be expressed as a percentage + or - error on the mean value or centre value.



There are many ways of treating data errors and these are just two possibilities.

Answer 2

You can solve for the energy balance at the Earth's orbit. Assume a 1m^2 flat surface facing the sun. Both sides emit into space. Energy in is about 1350 W/m^2. This results in T = 330 K The Earth is a bit more complex spectrally, so you'd need to integrate the spectral abosrption against the incoming energy spectrally, as well as modify the spectral emissivity. So, the answer to your question isn't quite so straightforward. The numbers do work out pretty close. The same surface at Pluto's orbit would be at 52 K. Again, a more detailed spectral calculation should get you to the ~30K temperature of Pluto. It'll actually take you at least 5 hrs to completely freeze with no sunlight, since your radiance is limited by surface area, and you can't radiate more than about 600W.

Answer 3

e=m-r

error= measurement-real value