Chapter 5: Errors in Chemical
Analysis
Overview
• Mean & Median
• Accuracy & Precision
• Types of Errors in Data
– Random Errors
– Systematic Errors
• A Mean Calculation Using Excel
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:
– Even numbered Data Set:
– Review Example 5.1
Median easily picked
Take mean of middle pair
Fig 5-1, p.91
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%
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 |
Fig 5-2, p.93
Fig 5-3, p.94
p86
p86
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.
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.
Types of Errors in Data
• Three Types of Systematic Errors
– Instrument errors
– Method errors
– Personal errors
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.
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.
p91
Excel Exercise 3: A Mean Calculation
• Construct the following in Microsoft Excel
p.100
p.101
p.102
p.102
Suggested Exercises
• HW Set 4:
5.1, 5.5, 5.8, 5.12