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# Statistics Puzzle watch

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1. A nice little stats puzzle for you...

Part I

If a quantity, x, is measured to be (10.3±0.1) m, and a constant a is known to be exactly 2.0 m, what are the percentage standard errors in:
(a) (x-a)^-1
(b) ln(x/a)

Part II

If another quantity, y, is measured to be (53.0±0.2) m, find the percentage standard errors in the combinations:

(a) x^2 + y^2
(b) xy
(c) x-2y

For part II, x is the same as part I. There's rep for the first one to do it correctly (all of it)! The answers will be posted each time a correct solution to a part of a question is posted. Good Luck!!!!!
2. 1 a)

(x-a) = 8.3 ±0.1 = between 8.2 and 8.4

1/8.2 = 0.12195
1/8.4 = 0.11905

=> (x-a)^-1 = 0.1205 ± 0.00145

i.e. 1.2% error
3. Part I

(a) 1.2%
(b) 0.6%
4. b) log (10.4/2) = 1.6486 (using natural logs)
log(10.2/2) = 1.6292

=> ln(x/a) = 1.6389 ± 0.009709

i.e. 0.5924 % error
5. OK... as there have been no advances in the last hour, a hint for part II is here:

If z is a function of two variables (x,y):

(error in z)^2 =
[(partial dz / dx)^2][(error in x)^2] + [(partial dz / dy)^2][(error in y)^2]

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Updated: May 8, 2004
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