119_2_Stat_Data_07F - II. Statistical Analysis of Data...

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1 II. Statistical Analysis of Data Significant Figures and Relative Accuracy Error or Uncertainty in Measurements Mean, Deviation, Confidence Interval Distribution Plots, Gaussian Distribution Curve Are Two Values Different? Rejection of Data Propagation of Uncertainty Chap. 3: Exercises: A, B, C Chap 4: Exercises: A, B (an exercise in Excel),E, F (a, b, c)
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2 Statistical Analysis of Data Significant Figures and Relative Accuracy Relative Accuracy, not number of digits 1.0026 5 sig figs 0.9936 4 sig figs Both given to ~ 1/10,000 1.007 ± 0.004 1.007 ± 0.010 or 1.01 ± 0.01 1.2763 1.2673 + 0.32 - 0.0008 1.60 1.2665 2.10*10 -4 3.6*10 -2 *3.6*10 -2 ÷ 2.10*10 - 4 7.6*10 -6 1.71*10 2
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3 Statistical Analysis of Data Error or Uncertainty in Measurements Determinate (Systematic) Error: 1. Constant error: X(Exp) - X(True) = δ Calibration error of instruments Blank correction in titration Solubility losses Background absorbance of solvent δ /X decreases as X increases Therefore, do experiments with different sample sizes 2. Proportional error: X(Exp) - X(True) = ε X(True) NaBr as contaminant in NaCl for Ag determination as AgCl Therefore, do experiments with different bottles of reagents
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4 Statistical Analysis of Data Error or Uncertainty in Measurements Indeterminate (Random) Error (Uncertainty) Limit of the technique. Cannot be eliminated. Not really error, but precision or repeatability of measurements. Precision = reproducibility of measurements Accuracy = agreement with “true” value
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5 Statistical Analysis of Data Mean, Deviation Average = (arithmetic) mean <X>= Σ X i /n Deviation = X i - <X> Range = Spread = X i (max) - X i (min) i i X X X X Average Deviation n n - - < = = Relative Deviation X X i i X X X X - < - = = <
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6 Statistical Analysis of Data Mean, Deviation Average (Relative Deviation) = Relative (Average Deviation) i X - X X Average (Relative Deviation) = n I I I I I I I I i X -X = nX I i X - X n Relative Average Deviation = X I i X -X = nX I
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7 Statistical Analysis of Data Standard Deviation TI 25, HP 20, Excel, TI 85(SX),TI 89 1 HP 48G, Mathcad, TI 85 (sX) 2 n X X Variance s use We n X X s i i < - = = 2245 - < - = 2245 2 2 ) ( 2 . 1 ) ( 1 σ
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8 Statistical Analysis of Data % Relative Standard Deviation or Coefficient of Variation ( 29 2 % % 100 1 i i X X s s RSD CV n X σ - 2245 = = = -
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Statistical Analysis of Data Volume of a pipet: Std dev = ±0.015, RSD {CV} = ±0.008 X i X i - <X> Deviation (X i - <X>)/<X> Relative Deviation 1.987 - 0.006 - 0.003 2.013 +0.020 +0.010
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119_2_Stat_Data_07F - II. Statistical Analysis of Data...

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