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

s (value average)2

n 1

s (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+002.00E-074.00E-076.00E-078.00E-071.00E-061.20E-061.40E-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!