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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. Calculating Standard Deviation in Excel Pooled Standard Deviation Propagation of Error Calculations Significant Figures.

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Chapter 6: Random Errors in Chemical Analysis

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  1. Chapter 6: Random Errors in Chemical Analysis CHE 321: Quantitative Chemical Analysis Dr. Jerome Williams, Ph.D. Saint Leo University

  2. Overview • Calculating Standard Deviation in Excel • Pooled Standard Deviation • Propagation of Error Calculations • Significant Figures

  3. 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%.

  4. p.118

  5. p.119

  6. p.120

  7. p.120

  8. p.122

  9. p.122

  10. 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.

  11. 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.

  12. 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.

  13. Table 6-6 p110

  14. Significant Figures • Review the rules for counting significant figures • Review the rules for determining significant figures in calculations • Review the rounding convention in text

  15. Figure 6-5 p116

  16. Suggested Problems • HW Set 5: 6.2, 6.7, 6.8, 6.9 (a,c,e), 6.18

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