Download Chapter 6: Random Errors in Chemical Analysis

Chapter 6: Random Errors in
Chemical Analysis
CHE 321: Quantitative Chemical Analysis
Dr. Jerome Williams, Ph.D.
Saint Leo University
Overview
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Calculating Standard Deviation in Excel
Pooled Standard Deviation
Propagation of Error Calculations
Significant Figures
Calculating Standard Deviation in Excel
• Calculating sample statistics in Excel
– Standard deviation uses STDEV() function
– Variance uses VAR() function
– Coefficient of Variation, also called percent relative
standard deviation, is obtained by taking the standard
deviation divided by mean, and that result is then
multiplied by 100%.
p.118
p.119
p.120
p.120
p.122
p.122
Pooled Standard Deviation
• Statistical testing (Chapter 7) based on sample standard
deviation. The better the s value, the greater the probability
of having correct results.
– As N increases (>20), the sample standard deviation value approaches
that of the population standard deviation.
• If one has several subsets of data, a better estimate of the
population standard deviation is obtained by pooling
(combining) the data into one global data set.
Statistical Treatment of Random Errors
• Pooled standard deviation (denoted by the letter spooled) is a
measure of the precision of a sample data set and is
calculated using the following equation.
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spooled = SQRT (SUM (xi – mean1)2 + (xi – mean2)2 + … / N1 + N2 + … - Nsubsets)
• Note: One degree freedom is lost for each data subset.
Propagation of Error Calculations
• Sometimes one must estimate the standard deviation of a
result that has been calculated from two or more
experimental data points, each having its own sample
standard deviation.
Table 6-6 p110
Significant Figures
• Review the rules for counting significant
figures
• Review the rules for determining significant
figures in calculations
• Review the rounding convention in text
Figure 6-5 p116
Suggested Problems
• HW Set 5: 6.2, 6.7, 6.8, 6.9 (a,c,e), 6.18