1. Lecture 5 Random Errors in Chemical Analysis - II

2. A measurement x 1, with   and    I am making a second measurement x 2 of the same analyte. Random!  It has the same  We do not know it! It has the same  As an estimate of my unknown  I will use average

3. ………… If I am making N measurements of the same value

5. Case 3: We know: Standard deviation  Real value ? Take N measurements; calculate average as with 95% probability Coinfidence interval (CI)

6. Case 4 We know nothing: Mean - ? Standard deviation -? Take N measurements; calculate average as Calculate standard deviation as Confidence interval? I do not know 

8. Case 4 We know nothing: Mean - ? Standard deviation -? Take N measurements; calculate average as Calculate standard deviation as with 95% probability Coinfidence interval (CI)

9. 68101214 16  =12.34 s=0.50 N=2 68101214 16N=3 68101214 16 68101214 16 N=4 N=6

10. 11.812.212.6  =12.34 s=0.50 N=6 11.812.212.6 11.812.212.6 N=15 N=60

13. I titrate an unknown solution using a class A 50 mL burette. My results show standard deviation of 0.05 mL. How many mesurements I need in order to get confidence interval of ±0.01 mL? N=2 N=4 N=9 N=20 N=120 U bur = 0.05 mL

15. A very simple rule: CIs overlap – the same CIs do not overlap - different