Working with values with uncertainties

[Askov]

Hi.
I am doing an uncertainty analysis and I need to be able to work with numbers and their associated uncertainties.

If we say I have the following:
a = 10+-0.5
b = 20+-0.7

And I need to find:
c = a + b
d = a * b
e = a / b

Is there a function in Excel that can easily add, multiply and/or divide values including the uncertainties?

The math behind it is somewhat simple, but will take up a lot of work (and carry the risk of making a mistakes) if I have to write the full formulas for these operations.

[dilipandey]

HI Askov,

Welcome to the forum.
addition (+) , multiplication (*) and division (/) available in Excel as separate function (operators)..are you looking all in one? I hope not.. the only thing here is that value of "a" can be 10 plus/minus 0.5 and value of "b" can be 20 plus / minus 0.7 and for this, you can use formula like Rand() with 10 or 20 to server plus / minus purpose.

Regards,
DILIPandey
<click on below * if this helps>

[Askov]

Hi DILIPandey.
I think you are misunderstanding me - I probably did not make myself fully clear.

When you want to add or subtract average values reported with their standard deviations, you don't simply add the standard deviations to produce the final standard deviation. Instead, you square the standard deviations, add them, then take the square root of the sum.

An example should make this clearer. Assume we have the following three values with their standard deviations

A = 1.67 +- 0.05
B = 5.23 +- 0.09
C= 1.88 +- 0.07

and we want to compute X = A+B-C. The actual addition of the values themselves is trivial:

1.67 + 5.23 - 1.88 = 5.02

To compute the standard deviation of the result, we must sum the squares of the errors and then take the sqaure root.

Stot = sqrt(0.052 + 0.092 + 0.072)
Stot = sqrt(0.0025+0.0081+0.0049)
Stot = 0.12

We would report the result of this sum as

X = 5.0+-0.1

My question is if there is a function in Excel that can do this, so I do not have to write out the full equation as this will be quite cumbersome for larger equations? Fx so I can write X = A+B-C and Excel will return 5.0+-0.1 as the result....

Also, do similar functions for multiplication and division exists?

Hope this makes things more clear...

Best regards,
Askov

[dilipandey]

yes.. this time its clear..
I believe there is no such function as per my knowledge.. but individual functions like sqrt and sum etc are there.. I would suggest you to create a master formula for all values.. and then you can change just the values in reference cells OR you can create a master template with formulas already there and then you just need to paste values everytime

Regards,
DILIPandey
<click on below * if this helps>