Error Analysis Flashcards
What is error in the context of measurement?
The difference between the measured value and the true value.
Define absolute error.
The magnitude of difference between true value and measured value of a quantity. Symbol= ∆x1 individual quantity
How is the true or mean value calculated?
By averaging the given quantities
X = (x1 + x2 + x3 + … + xN) / N
What is the formula for absolute error for a single measurement?
∆x1 = x - x1
What is the mean absolute error?
Averaging absolute errors in modules
∆X = (|∆x1| + |∆x2| + … + |∆xN|) / N
What is relative or fractional error?
∆x/x = Mean absolute error / Mean value
How is percentage error calculated?
Percentage error = (∆x/x) x 100
What happens to errors in addition and subtraction?
Errors in both addition and subtraction are always added.
What is the formula for error propagation in addition?
∆x = ∆a + ∆b
What is the formula for error propagation in subtraction?
∆x = ∆a + ∆b
What is the result of a measurement including error?
Result → x ± ∆x
What is the formula for error propagation in multiplication?
∆x/x = ∆a/a + ∆b/b
What is the formula for error propagation in division?
∆x/x = ∆a/a + ∆b/b
How is error calculated for quantities raised to a power?
∆x/x = p(∆a/a) + q(∆b/b) + r(∆c/c)
True or False: Absolute error can be negative.
False
What does the mean absolute error represent?
The average of the absolute errors from multiple measurements.
What is the significance of the modulus operation in mean absolute error calculation?
It ensures all errors are positive.
