Summary_03

# Summary_03 - Chapter 3. Propagation of Error 3.1...

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Chapter 3. Propagation of Error

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3.1 Measurement Error Error: systematic error (bias) and random error (uncertainty). Measured value = true value + bias + random error. Bias determines the accuracy of measuring and Uncertainty determines the precision of measuring. A measured value is a random variable with mean μ and standard deviation σ . Bias = μ – true value, Uncertainty = σ. If the bias of population has been reduced to a negligible level, then the measurements can be expressed as Measured value ± σ .
3.2 Linear Combination of Measurements If X is a measurement and c is a constant, then If X 1 , X 2 , …. ., X n are independent measurements and c 1 , c 2 , …. ., c n are constants, then X cX σ c σ = 2 2 2 2 2 2 2 1 .... ... 2 1 2 2 1 1 n n n X n X X X c X c X c σ c σ c σ c σ + + + = + + +

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Repeated Measurements If X 1 , X 2 , …, X n are n independent measurements, each with mean μ and uncertainty σ , then the sample mean is a measurement with mean and with uncertainty X μ = X n X σ =
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## This note was uploaded on 11/02/2010 for the course ENGR 320 taught by Professor Dr.nam during the Fall '10 term at SUBR.

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Summary_03 - Chapter 3. Propagation of Error 3.1...

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