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Error Bars in Normal Distributions
Error Bars in Column / Bar Graphs
http://chandoo.org/wp/2010/07/12/gantt-box-chart-tutorial-template/http://support2.dundas.com/OnlineDocumentation/winchart2005/ErrorBarsChart.html
Standard Deviation, s
(value average)2
n 1
(value average)2
n
Standard Deviation: A statistical measure of spread or variability. Computed as the root mean square (RMS) deviation of the values from their arithmetic mean.
Variance: The square of the standard deviation.
STDEV, sample of a largerpopulation
STDEVP, entire population
Average & Error Barsin Column Graphs
Compute Sigma
Compute Sigma
How to Add Error Bars
How to Add Error Bars
1
2 3
4
5
How to Add Error Bars
Type sigma here
Select the cell that contains the sigma value
Average & Error Barsin Bar Graphs
Average & Error Barsin Bar Graphs
Average & Error Barsin Bar Graphs
Bad example Better example
(X,Y) Scatter Graphs& Regression
How to Present (X,Y) Scatter Graphs, Compute Trendlines, and Extract Chemical
Information using Excel
Example: Chemical Kinetics & Equilibria SP10 Assign. #4 on Aspirin: Handout & online.
SP11 Assign. #4 on pH-Indicator: Handout & online.
AP11 Assignment #4
AP11 Assignment #4
AP11 Assignment #4
Your simulated spectrum will be the sum of the Gaussian functions that describe the absorbances of the three species: -- protonated dye-- neutral dye, and -- deprotonated dye.
AP11 Assignment #4
1.5 3.5 5.5 7.5 9.511.5
00.05
0.10.15
0.20.25
0.30.35
0.40.45
Gaussian Sums[C]
[D]
[A]
11.5
9
7
5
1.5
Wavelength (nm)Ab
sorp
tion
1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.510.5
11.50.00E+00
2.00E-07
4.00E-07
6.00E-07
8.00E-07
1.00E-06
1.20E-06
1.40E-06
Concentration vs. pH
[C][D][A]
pH
Conc
entr
ation
(M)
(X,Y) Built-In Functions
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data Quadratic Function
(X,Y) Data QF: Y-Axis Error Bars
1. Left click the graph line to which you want to add error bars.2-Mac: Control-click the selected line.2-PC: Left-click the selected line.3. Select “Format Data Series”.
(X,Y) Data QF: Y-Axis Error Bars
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4
5
(X,Y) Data QF: Y-Axis Error Bars
(X,Y) Data QF: Y-Axis Error Bars
(X,Y) Data QF: Types of Errors
The precise function was y = x2
The sample data were computed with: y = [x+0.3*RAND()]2 The x-values were assumed to be error-free
The fitted function was: y = 0.9937x2+ 0.3459xThe STDEV of the y-values is 0.62
Systematic error: All numbersin the sample will be too high!
Systematic error: There should not be a linear term.
This is were you notice the systematic error made (on purpose) in the sample data generation!
