Question 1181507: Determine the absolute deviation and the coefficient of variation.
𝑦=[200.432 (±0.002)]^1/2 / log(20.42 × 10^15(±0.06))
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the absolute deviation and coefficient of variation for the given expression:
**1. Calculate the value of y:**
y = sqrt(200.432) / log(20.42 × 10^15)
y ≈ 14.157 / 15.310
y ≈ 0.9246
**2. Calculate the uncertainty in y:**
To do this properly, we need to consider the uncertainties in both the numerator and the denominator. We'll use the formula for propagation of uncertainty through division:
(δy/y) = sqrt((δA/A)^2 + (δB/B)^2)
Where:
* A = 200.432, δA = 0.002
* B = 20.42 × 10^15, δB = 0.06 × 10^15
First, find the relative uncertainties:
* (δA/A) = 0.002 / 200.432 ≈ 0.00001
* (δB/B) = 0.06 × 10^15 / (20.42 × 10^15) ≈ 0.00294
Now, calculate the relative uncertainty in y:
(δy/y) = sqrt((0.00001)^2 + (0.00294)^2)
(δy/y) ≈ 0.00294
Finally, calculate the absolute uncertainty in y:
δy = (δy/y) * y
δy ≈ 0.00294 * 0.9246
δy ≈ 0.00272
**3. Express the result:**
y = 0.9246 ± 0.00272
**4. Calculate the coefficient of variation:**
Coefficient of variation = (δy / y) * 100%
Coefficient of variation = (0.00272 / 0.9246) * 100%
Coefficient of variation ≈ 0.294%
**Therefore:**
* **Absolute deviation:** ± 0.00272
* **Coefficient of variation:** ≈ 0.294%
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