Calculating the error of a ratio

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Hi,

I have two values with an error each (SD or S.E.M), and I need to find the ratio with an error.

E.g.

x = 200,000 - 6000 (S.E.M)

y = 50,000 - 1000 (S.E.M)

I need to find x/y so it would be 4 but how would I calculate the error?

Things I've tried:

Error(x)/x = 0.03

Error(y)/y = 0.02

Pooled S.E.M = Sqrt((0.03^2) (0.02^2)) = 0.036

0.036 is the ratio of the error so 0.036*4 = 0.144

So x/y = 4 - 0.144

Alternatively:

Max difference = (x error(x)) / (y-error(y))

= (200,000 6,000) / (50,000-1,000)

= 4.204

So x/y = 4 - (4.204-4)

= 4 - 0.204

Are either of these correct?

Any help at all would be greatly appreciated, cheers.

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RickH678

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