Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data14323.92 24.45 26.64 28.80 23.59 23.9824.53 24.48 27.63 27.99 23.37 23.5624.95 24.30 28.42 28.21 24.17 22.8024.76 24.60 25.16 28.00 23.48 23.2925.18 24.57 28.53 28.21 23.80 23.86Examine this data statistically and write a brief report on your conclusions.Issues you may wish to address include the presence of outliersin the samples, a summary of the descriptive statistics for each sample,and any evidence for a difference between the samples.Many of the problems that follow require accessto statistical tables. For your convenience,here are hyperlinks to the appendices containingthese tables.Appendix 3: Single-Sided Normal DistributionAppendix 4: Critical Values for the t-TestAppendix 5: Critical Values for the F-TestAppendix 6: Critical Values for Dixon’s Q-TestAppendix 7: Critical Values for Grubb’s Test4LSolutions to Practice ExercisesPractice Exercise 4.1Mean: To find the mean we sum up the individual measurements and divideby the number of measurements. The sum of the 10 concentrationsis 1405. Dividing the sum by 10, gives the mean as 140.5, or 1.40×10 2mmol/L.Median: To find the mean we arrange the 10 measurements from thesmallest concentration to the largest concentration; thus118 132 137 140 141 143 143 145 149 157The median for a data set with 10 members is the average of the fifth andsixth values; thus, the median is (141 + 143)/2, or 141 mmol/L.Range: The range is the difference between the largest value and the smallestvalue; thus, the range is 157 – 118 = 39 mmol/L.Standard Deviation: To calculate the standard deviation we first calculatethe difference between each measurement and the mean value (140.5),square the resulting differences, and add them together. The differencesare-0.5 2.5 0.5 -3.5 -8.5 16.5 2.5 8.5 -22.5 4.5and the squared differences are0.25 6.25 0.25 12.25 72.25 272.25 6.25 72.25 506.25 20.25The total sum of squares, which is the numerator of equation 4.1, is968.50. The standard deviation iss =968.5010 − 1= 10. 37 ≈ 10.4Variance: The variance is the square of the standard deviation, or 108.