1. Chapter 5: Errors in Chemical Analysis

2. Overview Mean & Median Accuracy & Precision Types of Errors in Data
Random Errors
Systematic Errors
A Mean Calculation Using Excel

3. Mean & Median
Mean is arithmetic average of data set; evaluated as follows:
Mean = Σ Xi / N
Median is the middle value of a data set when the data are arranged according to increasing or decreasing value
Odd numbered Data Set: Median easily picked
Even numbered Data Set: Take mean of middle pair
Review Example 5.1

4. Fig 5-1, p.91

5. Accuracy & Precision
Accuracy is the closeness of a measured value Xi to the true or accepted value Xt
Often expressed as either absolute error or relative error (percent, parts per thousand, or parts per million)
Absolute Error (E) = Xi - Xt
Relative Error (Er) = ((Xi - Xt ) / Xt ) * 100%

6. Accuracy & Precision
Precision describes the reproducibility of measurements (closeness of results to others) obtained in exactly the same way.
Three terms widely used to describe precision include standard deviation, variance, and coefficient of variation. All are functions of deviation from the mean.
Deviation from Mean (di) = |Xi – Mean |

7. Fig 5-2, p.93

8. Fig 5-3, p.94

9. p86

10. p86

11. Types of Errors in Data
Random Errors (Indeterminate Errors) affect measurement of precision.
Systematic Errors (Determinate Errors) affect accuracy of results.
Gross Errors occur as a result of human error and often lead to outliers (results that differ markedly from all other data in a set of replicate measurements.

12. Types of Errors in Data
Systematic Errors have a definite value and an assignable cause, and are of the same magnitude for replicate measurements made in the same way.
Systematic errors lead to bias in measurement results. Bias can be negative or positive in sign.

13. Types of Errors in Data Three Types of Systematic Errors
Instrument errors
Method errors
Personal errors

14. Types of Errors in Data
Systematic Errors may be either constant or proportional.
Constant errors are independent of the size of the sample being analyzed.
Proportional errors decrease or increase in proportion to the sample size.

15. Types of Errors in Data Detection of Systematic Errors
Instrument errors resolved through calibration of equipment.
Personal errors minimized by exercising care and self-discipline.
Method errors are the hardest to overcome; some ideas to overcome this one include using standard reference materials, independent analysis, running blank determinations, etc.

16. p91

17. Excel Exercise 3: A Mean Calculation
Construct the following in Microsoft Excel

18. p.100

19. p.101

20. p.102

21. p.102

22. Suggested Exercises
HW Set 4: 5.1, 5.5, 5.8, 5.12