Handout16-Statistics

Handout16-Statistics - CEM 834 STATISTICS FALL 2005 I....

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CEM 834 STATISTICS FALL 2005 I. Statistical Representation of Experimental Data Whenever multiple measurements are made of the same physical or chemical quantity, it is necessary to use statistical calculations to represent the mean value as well as the precision and accuracy of the measurements. A. The accuracy of experimental results can be expressed as 1. Absolute Error (e ) i μ - = i i x e where x i is the experimentally determined value and μ is the true or known value. Note that the error has a sign associated with it that indicates direction. 2. Relative Error ) ( i ε ε μ μ i i x = - which is often expressed in %, ppt, ppm, etc. B. The precision of experimental results can be expressed as 1. Deviation or Residual ( 29 d i d x x i i = - where x is the mean value, which is given by x x n and n is the number of measurements. i i 1 n = =
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2. Relative Deviation ) ( i δ δ i i x x x = - 3. Standard Deviation ) ( σ ( 29 σ μ = - = x n i 2 i n 1 where μ is the true or known value of the population mean, which is not generally
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Handout16-Statistics - CEM 834 STATISTICS FALL 2005 I....

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