Chapter 6: Random Errors in Chemical Analysis

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 (gt20), 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