QCA7e_ch04_szb_handouts

# QCA7e_ch04_szb_handouts - Daniel C. Harris Quantitative...

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1 Quantitative Chemical Analysis Seventh Edition Quantitative Chemical Analysis Seventh Edition Chapter 4 Statistics Copyright © 2007 by W. H. Freeman and Company Daniel C. Harris Daniel C. Harris Is my blood cell count high? • Statistics gives us tools to accept conclusions that have a high probability of being correct and to reject conclusions that do not.

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2 Gaussian Distribution • If an experiment: – is repeated many times – the errors in it are purely random the results tend to cluster symmetrically about the average value • The more times the experiment is repeated, the more closely the results approach an ideal smooth curve called the Gaussian distribution Gaussian Distribution
3 Why Statistics? • We cannot always make so many measurements in a lab experiment to make a smooth curve. • However, from the small set of results, we can estimate the statistical parameters that describe the large set. Mean Value • The arithmetic mean , – also called the average – is the sum of the measured values divided by n, the number of measurements:

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4 Standard Deviation •The standard deviation , s, measures how closely the data are clustered about the mean. • The smaller the standard deviation, the more closely the data are clustered about the mean. Some More Definitions • The quantity (n 1) seen before is called the degrees of freedom . • The square of the standard deviation is called the variance . • The standard deviation expressed as a percentage of the mean value is called the relative standard deviation or the coefficient of variation: ( ) x s × = % 100
5 Example • Find the average and the standard deviation for 821, 783, 834, and 855. •So lu t ion : –Mean:

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6 Standard Deviation and Probability • For a finite set of data, we approximate μ by x and σ by s . A gaussian function
7 Normal Error Curve • A Gaussian curve whose area is unity is called a normal error curve. – In this case: the probability of measuring

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## This note was uploaded on 01/29/2009 for the course CHEM CHEM 141 taught by Professor Balintsztaray,ph.d during the Fall '08 term at Pacific.

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QCA7e_ch04_szb_handouts - Daniel C. Harris Quantitative...

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