plz, help me with this question 2 ERROR PROPAGATION. The coefficient of variatio
ID: 2926716 • Letter: P
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plz, help me with this question
2 ERROR PROPAGATION. The coefficient of variation of an uncertain measurement is defined as the standard deviation divided by the mean, = standard deviation ÷ me an = s /m. if we let z-s/m be the coefficient of variation, and m and s be the mean and standard deviation, respectively This is sometimes called, the proportional error: We know from the lectures that if z , then the squared coefficient of variation of z equals the sum of the squared coefficients of variation of r and y. In words, this says that proportional errors in a product propagate as the sum of their squares. My friend Bubba argues that since x2 -xx, the proportional error in x2 must be, 2Explanation / Answer
The correct format of proportional error for x^2 is the one specified by the first friend
Porportional error of z = sqrt(2) * Proportional error of x
.
The reason why this is correct is as follows:
As per the definition of the proportional error : it is equal to standard deviation divided by mean. The impact on standard error is reflected in the value of proportional error
thus when we get Sz^2 = 2 * Sx^2
we get Sz = sqrt(2) * Sx
thus this is the same relation as proportional error
.
The friend who is wrong is wrong because of incorrectly defining Proportional error.
he explains proportional error as derivative of x, which is not the true method to represent of calculate proportional error.
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