# Confidence interval considering the division of 2 means with different CIs? Statistics

I have the mean and its confidence interval (standard deviation and size of its sample) of 2 different data A and B. I want to divide A/B and get the confidence interval of its division. Is there a formula for that?

For example, I want to divide time (400 s +/- 20s) per size (10 m +/- 3m). What's the result, considering confidence interval?

• Wrong stack? This is for the software Mathematica. Perhaps CrossValidated stack is what you're after?
– ciao
Jun 23 '20 at 19:31
• Take a look at Propagation of uncertainty - example formulae? Jun 23 '20 at 19:39

In version 12 of Mathematica, there is the function Around which does what the link in the comment by @MarcoB does. However, Around assumes that the covariance term is zero.

Statisticians use the term "Delta Method" rather than "Propagation of error" or "Propagation of uncertainty".

For your example if 20 and 3 represent standard errors:

Around[400, 20]/Around[10, 3]
(* Around[40., 12.165525060596439] *)


More generally:

Around[m1, s1]/Around[m2, s2]
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