# Lecture_overheads_-_Ch04 (1) - CHEM 321 – Quantitative...

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHEM 321 – Quantitative Analysis Ch. 4 – Statistics 4-1 Gaussian Distribution 4-2 Confidence Intervals 4-3 Comparison of Means with Student’s t 4-6 Grubbs Test for an Outlier 4-7 Method of Least Squares 4-1 Gaussian Distribution Requirements • Multiple (replicate) experimental measurements • Assumes only random errors in measurements ( no determinate errors ) Results • Histogram (# occurrences versus measured value) should give symmetrical, bell-shaped curve • Data will “cluster” or center around some value ( mean ) • Data will show some “spread” ( uncertainty ) Problems • Inability to make sufficient number of replicate measurements ( n is finite ) • Non-random errors may be present (determinate errors, poor accuracy) Mean Standard Deviation Mean is best estimate of center of distribution (estimate of “true” value ) Standard deviation is the best estimate of how closely data are clustered about the mean (estimate of uncertainty or precision of the measurement) EXCEL formulas Mean: “ = average(A1:A5)” Std dev: “ = stdev(A1:A5)” = ∑ n x x n i i ( 29 1 2-- = ∑ n x x s i i n – 1 = “ Degrees of freedom ” ( 29 1 2-- = ∑ n x x s i i Theoretical Gaussian curve (true mean and uncertainty are unknown) Can estimate mean and uncertainty from experimental data – x = 845.2 s = 94.2 2 Gaussian curves with same mean but different standard deviations Consider case of 2 students analyzing the SAME unknown OR an analyst using 2 different methods to analyze the SAME unknown Comparing means and standard deviations is useful Its impossible to judge accuracy from this information ( μ not known, no info as to which data set is more correct) BUT one can compare precision of two data sets (s) In reporting a result, we typically give the mean and the standard deviation Remember to follow the “real rule” for SF here s x ± Example mean value and its uncertainty 845.2 ± 94.2 SF incorrect (8.5 ± 0.9) x 10 2 # SF clear (follow real rule for SF) Data that conform to a Gaussian distribution are said to be “normally distributed” A Gaussian distribution is an ideal, theoretical curve that is symmetrical about the mean Gaussian distribution equation ( 29 -- = 2 2 2 exp 2 1 σ μ π σ x y exp = base of natural log (2.7183) σ = population standard deviation μ = population mean (“true” value) Keep in mind that...
View Full Document

{[ snackBarMessage ]}

### Page1 / 21

Lecture_overheads_-_Ch04 (1) - CHEM 321 – Quantitative...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online