EGR 105 Foundations of Engineering I

Excel Part II More on PlottingSection 8 Fall 2013

EGR 105 Foundations of Engineering I

Excel Part II Topics• Data (engineers collect and use)

– Viewing– What is in the data?– Plotting Data…some ways to look at data

• Background on Plot Types• Transforming data to Log10

• Using Log10 Scales• Homework Assignment

Engineering and Data

• For Engineers, Data…– is useful– often routinely collected– requires interpretation– is used in a variety of ways– can be complex and difficult to work with

Data Can Be Complicated

Viewing Data• Recorded data can show a variety of

important trends and patterns• Plotting can provide insight

– There are different ways to view the data– It is important how data are presented – Often want to see data details on one plot

• Useful for developing equations• Will cover this topic next time in Excel Part III

What is in the Data?• When you have a set of data, ask…

– What do these data tell me?– Is there a trend…a relationship….?– How do the data describe reality?

• Not always obvious – Sometimes requires different looks– Plotting of data can be very useful

Presentation of x-y Data• Independent versus dependent

variables

y

y = f(x) xindependent

depe

nden

t

Simple PlottingGenerate X and Y data to Plot

Common Types of Plots Example: f(x) = y = 3x2

(plots for equations and/or data)

0 1 2 3 4 5 6 7 8 9 100

50100150200250300350

X

Y

1 100

50100150200250300350

Log (X)

Y

0 1 2 3 4 5 6 7 8 9 101

10

100

1000

X

Log

(Y)

Semi-log : Log (Y)

Cartesian

Semi-log : Log (X)

1 101

10

100

1000

Log (X)

LogY

Log-Log : Log (X)-Log (Y)

Excel Part II Topics• Data (engineers collect and use)

– Viewing– What is in the data?– Plotting Data…some ways to look at data

• Background on Some Useful Plot Types• Transforming data to Log10

• Using Log10 Scales• Homework Assignment

Lets Review These Plots• How were they created?• What is

– a linear plot– a semi-log plot– a log-log plot– a logarithmic scale

• Note that here we use Log10

Linear Scale

x y=f(x)0.00 0.000.10 0.010.20 0.030.30 0.100.40 0.230.50 0.410.60 0.680.60 0.680.80 1.480.90 2.041.00 2.721.50 8.182.00 17.892.50 32.813.00 53.863.50 81.894.00 117.725.00 215.926.00 354.436.50 440.587.00 538.908.00 774.739.00 1067.0710.00 1420.94

0 1 2 3 4 5 6 7 8 9 100

200

400

600

800

1000

1200

1400

1600

x

f(x)

Note: Cannot see details of these points

Take Log10 of x-data

x Log (x) y=f(x)0.00 --- 0.000.10 -1.00 0.010.20 -0.70 0.030.30 -0.52 0.100.40 -0.40 0.230.50 -0.30 0.410.60 -0.22 0.680.60 -0.22 0.680.80 -0.10 1.480.90 -0.05 2.041.00 0.00 2.721.50 0.18 8.182.00 0.30 17.892.50 0.40 32.813.00 0.48 53.863.50 0.54 81.894.00 0.60 117.725.00 0.70 215.926.00 0.78 354.436.50 0.81 440.587.00 0.85 538.908.00 0.90 774.739.00 0.95 1067.0710.00 1.00 1420.94

-1 0 10

200

400

600

800

1000

1200

1400

1600

Log (x)

f(x)

Note: Cannot see details of these points

Observe: Log (0) undefined Semi-Log Plot

Take Log10 of y-data

x f(x) Log (f(x))0.00 0.00 ---0.10 0.01 -2.28398730.20 0.03 -1.46570300.30 0.10 -0.98703730.40 0.23 -0.64741860.50 0.41 -0.38398990.60 0.68 -0.16875290.60 0.68 -0.16875290.80 1.48 0.17086580.90 2.04 0.30991271.00 2.72 0.43429451.50 8.18 0.91296022.00 17.89 1.25257882.50 32.81 1.51600763.00 53.86 1.73124453.50 81.89 1.91322484.00 117.72 2.07086325.00 215.92 2.33429196.00 354.43 2.54952896.50 440.58 2.64402217.00 538.90 2.73150918.00 774.73 2.88914769.00 1067.07 3.028194610.00 1420.94 3.1525763

0 1 2 3 4 5 6 7 8 9 10

-3

-2

-1

0

1

2

3

4

x

Log

(f(x

))

Observe: Log (0) undefined

Semi-Log Plot

Take Log10 of x-data and y-data

x Log (x) y=f(x) log (f(x))0.00 --- 0.00 ---0.10 -1.00 0.01 -2.28398730.20 -0.70 0.03 -1.46570300.30 -0.52 0.10 -0.98703730.40 -0.40 0.23 -0.64741860.50 -0.30 0.41 -0.38398990.60 -0.22 0.68 -0.16875290.60 -0.22 0.68 -0.16875290.80 -0.10 1.48 0.17086580.90 -0.05 2.04 0.30991271.00 0.00 2.72 0.43429451.50 0.18 8.18 0.91296022.00 0.30 17.89 1.25257882.50 0.40 32.81 1.51600763.00 0.48 53.86 1.73124453.50 0.54 81.89 1.91322484.00 0.60 117.72 2.07086325.00 0.70 215.92 2.33429196.00 0.78 354.43 2.54952896.50 0.81 440.58 2.64402217.00 0.85 538.90 2.73150918.00 0.90 774.73 2.88914769.00 0.95 1067.07 3.028194610.00 1.00 1420.94 3.1525763

-1 0 1

-4

-3

-2

-1

0

1

2

3

4

Log (x)

Log

(f(x

))

Note: Now can see details of these points

Observe: Log (0) undefined

Log-Log Plot

Excel Part II Topics• Data (engineers collect and use)

– Viewing– What is in the data?– Plotting Data…some ways to look at data

• Background on Plot Types• Transforming data to Log10

• Using Log10 Scales• Homework Assignment

Easier Way

• Create plots using Log10 scales– No need to convert any of the data– By hand on paper (available in stores)

• Semi- Log10 paper• Log10-Log10 paper

– Software packages• Excel• MatLab (in EGR 106 next semester)• other

Plot Using Log10 Scale for x

x y=f(x)0.00 0.000.10 0.010.20 0.030.30 0.100.40 0.230.50 0.410.60 0.680.60 0.680.80 1.480.90 2.041.00 2.721.50 8.182.00 17.892.50 32.813.00 53.863.50 81.894.00 117.725.00 215.926.00 354.436.50 440.587.00 538.908.00 774.739.00 1067.0710.00 1420.94

0

200

400

600

800

1000

1200

1400

1600

x

f(x)

Semi-Log Plot

Observe: No zero on Log scale - Log (0) undefined

Note: Scale variation is logarithmic

Plot Using Log10 Scale for y

0 1 2 3 4 5 6 7 8 9 100.001

0.010

0.100

1.000

10.000

100.000

1000.000

10000.000

x

f(x)

x y=f(x)0.00 0.000.10 0.010.20 0.030.30 0.100.40 0.230.50 0.410.60 0.680.60 0.680.80 1.480.90 2.041.00 2.721.50 8.182.00 17.892.50 32.813.00 53.863.50 81.894.00 117.725.00 215.926.00 354.436.50 440.587.00 538.908.00 774.739.00 1067.0710.00 1420.94

Semi-Log Plot

Observe: No zero on Log scale - Log (0) undefined

Note: Scale variation is logarithmic

Plot Using Log10 Scale for x and y

x y=f(x)0.00 0.000.10 0.010.20 0.030.30 0.100.40 0.230.50 0.410.60 0.680.60 0.680.80 1.480.90 2.041.00 2.721.50 8.182.00 17.892.50 32.813.00 53.863.50 81.894.00 117.725.00 215.926.00 354.436.50 440.587.00 538.908.00 774.739.00 1067.0710.00 1420.94

0.1 1.0 10.00.001

0.010

0.100

1.000

10.000

100.000

1000.000

10000.000

x

f(x)

Log-Log Plot

Observe: No zero on Log scale - Log (0) undefined

Note: Scale variation is logarithmic

Note: Scale variation is logarithmic

Excel Part II Topics• Data (engineers collect and use)

– Viewing– What is in the data?– Plotting Data…some ways to look at data

• Background on Plot Types• Transforming data to Log10

• Using Log10 Scales• Homework Assignment

Homework Assignment #4

• See HW4 on course web site– Import historical data for computer memory

prices into spreadsheet– Determine cost in $s/megabyte for each year– Plot data two different ways

• Linear scale• Semi-log scale• Discussion of details found in results

Homework Assignment #4

Submission ProceduresSubmit your Excel Spreadsheet with:- all imported and calculated data - each of the two plots- discussion embedded in a text boxSend as an email attachment to Prof. Sadd with the subject line egr105_4 (no spaces). Due Date: October 24.