Lecture_Chapter 4_Propagation of Error.pdf

Chapter 4 Evaluating Analytical Data Propagation of Error Analytical Chemistry Lecture 2100-01 Dr. Susan Verberne-Sutton Introduction to Chemical Statistics Mean) Median: Mode: Spread – Range: Standard Deviation: Percent Relative Standard De...

Chapter 4 Evaluating Analytical Data Propagation of Error Analytical Chemistry Lecture 2100-01 Dr. Susan Verberne-Sutton Introduction to Chemical Statistics Mean) Median: Mode: Spread – Range: Standard Deviation: Percent Relative Standard Deviation: Variance:  Accuracy vs. Precision [Error vs. Variance] Accuracy deals with the difference between real and expected data (e & er) Precision deals with the ‘distribution’ of data (s & s2) Indeterminate Errors- Determinate errors Calculating Error Absolute Error: e – Percent Relative Error: Sampling: Method: Measurement: Personal: Calculating Deviation (Variance) Penny Mass (g) 1 3.080 Calculate 2 3.094 3 3.107 Calculate the median 4 3.056 5 3.112 Calculate the mode 6 3.174 7 3.198 Calculate the standard deviation: Calculate the percent relative standard deviation: Calculate variance: Error & Deviation vs. Uncertainty Error is the difference between the actual and accepted value (accuracy) Standard Deviation is the spread of measurements about the mean Uncertainty expresses both and is propagated! How do we combine error and standard deviation to gain uncertainty? Number Volume (mL) Number Volume (mL) 1 10.002 6 9.983 2 9.993 7 9.991 3 9.984 8 9.990 4 9.996 9 9.988 5 9.989 10 9.999 Propagation of Uncertainty: Addition and Subtraction Propagation of Uncertainty: Multiplying & Dividing If: R = A x B / C Use the following equation to solve for the ‘relative uncertainty’ sR 2 2 2 = sA + sB + sC R A B C The quantity of charge, Q, in coulombs passing through an electrical circuit is Q = I x t where I is the current in amperes and t is the time in seconds. When a current of 0.15 ± 0.01 A passes through the circuit for 120 ± 1 s, what is the relative uncertainty? What is the absolute uncertainty? Challenge