Chapter 6: Random Errors in Chemical Analysis

CHE 321: Quantitative Chemical AnalysisDr. Jerome Williams, Ph.D.

Saint Leo University

Overview

• 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%.

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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.

• 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