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Chem 212!

Lecture 4!

Sept. 14/2016!

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How to use stats controls on calculator:!

stats mode!

2nd function mode!

M+ for adding data points!

RCL then xbar and sx!

clear= 2nd function CA!

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Describing the variation in large data sets:!

-make the same measurement many time... aka replicates!

-Plot the data from measurements you will get normal Gaussian distribution!

-+/- 1SD 68% within 1 std. dev of the mean!

-16% on either side, tails !

-+/- 2 std.dev area is 95.4% within mean!

"-problem resulting 2 std. dev reports larger range thus less value in number!

-95% area is within 2 std.dev!

-99% area is within 3 std.dev!

-If the data set is large then the data set describes the population!

"-the average is mu

"-std. dev is sigma!

-If data set is small then data describes a sample!

"-the average is xbar!

"-std. dev is s

* we use xbar and s to predict mu and sigma!

-Systematic error does not change to shape of the curve it changes the position along the x-axis!

-Eﬀect of change in Precision, Std. dev changes but the mean does not change!

"-conﬁdence interval aﬀected!

-mu and sigma are the true values for the population!

-the larger the n, the better the sample estimates the population!

-We will measure replicates, calculate xbar and s and use known characteristics of Gaussian distributions to make

conclusions about our data!

-We assume that analytical results have random error and apply the concepts from Normal or Gaussian statistics

to interpret our results!

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Stats tools:!

Conﬁdidence Interval:!

Stating results for an unknown sample !1.

Stating accuracy of results for a known sample!2.

Comparison of 2 data sets:!

Comparison of means t test ( news an F test and then a t test)!1.

Comparison of diﬀerences t test- choice of 2 types of t test!2.

Rejecting a bad data point!

Grubbs test!1.

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Conﬁdence Interval: Estimate true value from our experimental data!

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mu=xbar+/- t*S/n^1/2!

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