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Lecture 11B

Using ExcelChapter 8

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Example of an Excel Worksheet

Measured Volts Measured Resistance Computed Current(Volt) (Ohm) (Amps)

10 100 0.112 100 0.1211 100 0.1110 100 0.110 100 0.112 100 0.1211 100 0.1111 100 0.11

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Starting Excel

Figure 1-2,page 1.04

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The Excel Window Tool bar Formula bar Worksheet window

Columns and Rows Cells

Pointer Sheet tabs

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Moving Around a Worksheet Use the mouse Use the keyboard

Arrow keys Page Up Page Down Home Crtl + Home F5

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File Open...

Open 1-OhmsLaw.xls

Figure 1-8,page 1.11

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Some Basic Excel Stuff Learn how to enter text, values,

formulas, and functions Describe a range of cells Perform what-if analysis Learn how to use online Help Demonstrate how to print a

worksheet

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Entering Information Text - letters, symbols, numbers,

and spaces Values - numbers that represent a

quantity Formulas - used to calculate values Functions - special pre-written

formulas

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Range—used in functions Range - a group of cells: A1:C4

Figure 1-16,Page 1.19

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Saving a Workbook File Save As...

Figure 1-19,Page 1.23

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Playing “What-if?” Change a value in a cell Excel automatically recalculates

the worksheet

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Correcting Mistakes Before you press the Enter key

Use the Backspace key After you pressed the Enter Key

Double click on the cell to put it in Edit mode

Don’t use the Space bar to clear a cell

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Getting Help Microsoft Excel Help

Contents Answer Wizard Index

Show/Hide the Office Assistant What’s This? Office on the Web About Microsoft Excel

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Printing the Worksheet File Print...

Figure 1-28,Page 1.32

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Closing and Exiting File Close File Exit

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Intermediate Objectives List the components of a well

designed worksheet Understand “Order of Precedence” Demonstrate several methods for

copying information Understand Relative vs Absolute

Cell Referencing Change the name of the worksheet

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A Well Designed Worksheet Clearly identifies its goal Presents information in a clear,

well organized format Includes all necessary data to

produce the intended results

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Developing the Worksheet Determine the worksheet’s purpose Enter the data and formulas Test the worksheet Correct errors and make modifications Document the worksheet Improve the appearance Save and print the completed

worksheet

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Planning the Worksheet What is the goal of the worksheet? What data is needed to calculate the

results? What calculations are needed? EXAMPLE—Calculate density of air as a

function of temperature from 0-50C in 5 degree steps

=P/RT P=stnd atmosphere 101.3kPa R=gas constant for air 286.9 J/kg-K T=temp in Kelvins

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Building the Worksheet Establish the layout Enter the data Enter the formulas See 2-AirDensity.xls example

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Entering Labels Helps to identify the cells where

you will enter the data and formulas

Alignment is left justified, and spill into empty cells to the right

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Entering Data Values can be:

Numbers Formulas Functions

The data is the information you need to perform the calculations

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Entering Formulas Formulas are equations that

perform a calculation An = sign at the beginning of a cell

indicates you are entering a formula If formulas contain more than one

operator, Excel performs the calculation according to the standard order of precedence

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Order of Precedence Predefined rules used to perform a

calculation:

3 + 4 * 5 = ?

Is the answer 35 or 23?

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Order of Precedence (continued)

Exponent: ^ Multiplication and Division: * and / Addition and Subtraction: + and -

3 + 4 * 5 = 23

(3 + 4) * 5 = 35

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Copying Formulas Menu Commands Toolbar buttons Fill Handle

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AutoSum Button Automatically creates a formula

that contains the SUM function Looks at the cells adjacent to the

active cell and guesses which range of cells you want to sum

Excel’s guess is displayed

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Entering Functions Type the function by hand Use the Paste Function

button

Do the example in 3-Functions.xls

Figure 2.17,page 2.17

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Relative vs Absolute Reference Relative Cell Reference

= A5*B5 Absolute Cell Reference

= $A$5*$B$5

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Relative vs Absolute References when Copying Formulas

Relative Cell References - cell references change when they are copied

Absolute Cell References - cell references do not change when they are copied

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Mixed References Part of the reference is absolute

and part is relative:

$A5

Do the example in4-AbsoluteVsRelative.xls

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Copying using Copy & Paste Select the cell or cells to be copied Select Edit Copy Select the cell or cells you want to

replace Select Edit Paste

The copied cells are placed in the Clipboard, and can be pasted many

times.

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Renaming the Worksheet Double click on the worksheet tab Enter the new name

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Excel Plotting Skills Learn to use tables and graphs as

problem solving tools Learn and apply different types of

graphs and scales Prepare graphs in Excel Be able to edit graphs

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Plotting Data Independent Variables

“The Cause” X-Axis on Graphs (abscissa) Left Columns on Tables

Dependent Variables “The Effect” Y-Axis on Graphs (ordinate) Right Columns on Tables

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Question

The speed of sound in air depends on the temperature, humidity, and air pressure. What are the independent variables? …dependent variables?

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Table and Graph Requirements

Label the axes on your graphs. Include units on the axes and on

column headings. Use landscape graphs.

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Proper Use of Tables & Graphs

Height H (m)

Temp T (C)

Pressure P (kPa)

0 15.0 101.3 300 12.8 97.7

600 11.1 94.2

0

2

4

6

8

10

12

14

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0 500 1000 1500Height (m)

Tem

per

atu

re (

C)

0

20

40

60

80

100

120

140

160

Pre

ssu

re (

kPa)

Temp

Pressure

You can copy straight intoyour final report!

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Tables Tables should always have:

Title Column headings with brief descriptive name,

symbol and appropriate units. Numerical data in the table should be written

to the proper number of significant digits. The decimal points in a column should be aligned.

Tables should always be referenced and discussed (at least briefly) in the body of the text of the document containing the table.

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Table Example

Temperature and Pressure ofWidgets at Various Heights

Height H (m)

Temp T (C)

Pressure P (kPa)

0 15.0 101.3 300 12.8 97.7 600 11.1 94.2

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Graphs Proper graphing of data involves

several steps: Select appropriate graph type Select scale and gradation of axes,

and completely label axes Plot data points, then plot or fit

curves Add titles, notes, and or legend

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Graphs - Types

Travel Expenses

02468

1012141618

Fo

od

Ga

s

Mo

tel

Exp

ense

s ($

)

1. Pie Chart 2. Bar Graph

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Graphs - Types

4. Line Graph

0

2

4

6

8

10

12

14

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0 500 1000 1500Height (m)

Tem

per

atu

re (

C)

0

20

40

60

80

100

120

140

160

Pre

ssu

re (

kPa)

Temp

Pressure

1

2

3

4

5

6

7

01234567

8

02468101214

Object 1Object 2

Bod

y T

emp

erat

ure

(0C

Speed (m/s) Dis

tanc

e (m

)

3. 3-D Graph

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Graphs Each graph must include:

A descriptive title which provides a clear and concise statement of the information being presented

A legend defining point symbols or line types used for curves needs to be included

Labeled axes Graphs should always be

referenced/discussed in the body of the text of the document containing the table.

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Titles and Legends Each graph must be identified with

a descriptive title The title should include clear and

concise statement of the information being presented

A legend defining point symbols or line types used for curves needs to be included

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Axis Labels Each axis must be labeled The axis label should contain the

name of the variable and its units. The units can be enclosed in

parentheses, or separated from the label by a comma.

Length (km)

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Gradation Scale gradations should be

selected so that the smallest division of the axis is an integer power of 10 times 1, 2, or 5.

Exception is units of time.Scale Graduations,Smallest Division=1

Acceptable

Scale Graduations,Smallest Division=3.33

Not Acceptable

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Data Points and Curves Data Points are plotted using symbols

The symbol size must be large enough to easily distinguish them

A different symbol is used for each data set

Data Points are often connected with lines A different line style is often used for

each data set

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ExampleVelocity of Three Runners

During a 5 km Race

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Building a Graph In Excel Select the data that you want to include in the chart

by dragging through it with the mouse. Then click the Chart Wizard

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Choose XY (Scatter), with data connected by lines if desired.

Click “Next”

Building the Graph

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Building the Graph Make sure that the

series is listed in columns, since your data is presented in columns.

Click the Series tab to enter a name for the data set, if desired.

Choose “Next”

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Building the Graph Fill in Title and Axis information “Next”

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Building a Chart Select “As new sheet” to create the chart on it’s own sheet

in your Excel file, or “As object in” to create the chart on an existing sheet

“Finish”

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Creating a Secondary Axis This is useful when the data sets cover very

different ranges. Right click on the line

(data series) on the chart that you want to associate with a secondary axis.

Select “format data series”

Select the Axis tab, then “Plot series on secondary axis” as shown.

“OK”

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Editing/Adding Labels Now you can go back to the “chart options” to add labels

Click the chart in a blank area, then either right click and select chart options or choose chart options from the “Chart” menu

Fill in or edit the axes labels, title, etc.

Click “OK”

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Result

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Graphical Analysis and Excel

Solving Problems UsingGraphical Analysis

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RAT 5.1 Close you books, notes and laptops.

Turn off computer monitors.

As a TEAM, you have 3 minutes to answer the following question.

Name the type of function that plots as a straight line on: A) a semi-log graph B) a log-log graph

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Learning Objectives Learn to use tables and graphs as

problem solving tools Learn and apply different types of graphs

and scales Prepare graphs in Excel Be able to edit graphs Be able to plot data on log scale Be able to determine the best-fit

equations for linear, exponential and power functions

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Exercise Enter the following table in Excel

You can make your tables look nice by formatting text and borders

Independent Variable, x

Dependent Variable, y1

Dependent Variable, y2

1 1 1

2500 10 50 5000 100 100

7500 1000 150

10000 10000 200

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Axis Formats (Scales) There are three common axis formats:

Rectilinear: Two linear axes Semi-log: one log axis Log-log: two log axes

Length (km)

1 km 10 km

Log scale:

1 km

Length (km)

Linear scale:

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Use of Logarithmic Scales A logarithmic scale is normally

used to plot numbers that span many orders of magnitude

1 10 100 1000 10000

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Creating Log Scales in Excel

Exercise (2 min): Create a graph using only x and y1.

New Graph

0

2000

4000

6000

8000

10000

12000

0 2000 4000 6000 8000 10000 12000

x

y1 y1 data

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Creating Log Scales in Excel Now modify the graph so the data

is plotted as semi-log y This means that the y-axis is log scale

and the x-axis is linear. Right click on the axis to be

modified and select “format axis”

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Creating Log Scales in Excel

On the Scale tab, select logarithmic

“OK” Next, go to Chart

Options and select the Gridlines tab. Turn on (check) the Minor gridlines for the y-axis.

“OK”

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Result: Graph is straight line.

New Graph

1

10

100

1000

10000

0 2000 4000 6000 8000 10000 12000

x

y1 y1 data

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Exercise (10 min) Copy and Paste the graph twice. Modify one of the new graphs to be

semi-log x Modify the other new graph to be

log-log Note how the scale affects the

shape of the curve.

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Equations The equation that represents a straight line

on each type of scale is: Linear (rectilinear): y = mx + b Exponential (semi-log): y = bemx or y = b10mx

Power (log-log): y = bxm

The values of m and b can be determined if the coordinates of 2 points on THE BEST-FIT LINE are known: Insert the values of x and y for each point in the

equation (2 equations) Solve for m and b (2 unknowns)

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Equations (CAUTION) The values of m and b can be

determined if the coordinates of 2 points on THE BEST-FIT LINE are known.

You must select the points FROM THE LINE to compute m and b. In general, this will not be a data point from the data set. The exception - if the data point lies on the best-fit line.

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Consider the data set:X Y1 42 83 104 125 116 167 188 199 20

10 24

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Which data points should be used to determine the equation of this best-fit line?

Example of Best-Fit Line

0

5

10

15

20

25

30

0 2 4 6 8 10 12

X, Independent Variable (No Units)

Y, D

ep

en

de

nt

Va

ria

ble

(N

o U

nit

s)

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Example Points (0.1, 2) and (6, 20) are taken

from a straight line on a rectilinear graph.

Find the equation of the line. Solution:

2 = m(0.1) + b a)20 = m(6) + b b)

Solving a) & b) simultaneously:m = 3.05, b = 1.69

Thus: y = 3.05x + 1.69

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Pairs Exercise (10 min) FRONT PAIR:

Points (0.1, 2) and (6, 20) are taken from a straight line on a log-log graph.

Find the equation of the line.

BACK PAIR: Points (0.1, 2) and (6, 20) are taken from a

straight line on a semi-log graph. Find the equation(s) of the line.

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Interpolation Interpolation is the process of estimating a

value for a point that lies on a curve between known data points Linear interpolation assumes a straight line

between the known data points One Method:

Select the two points with known coordinates Determine the equation of the line that passes

through the two points Insert the X value of the desired point in the

equation and calculate the Y value

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Individual Exercise (5 min) Given the following set of points,

find y2 using linear interpolation.(x1,y1) = (1,18)(x2,y2) = (2.4,y2)(x3,y3) = (4,35)

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A Baseball Problem A runner is on 3rd base, 90 ft from home plate. He

can run with an average speed of 27 ft/s. A ball is hit to the center fielder who catches it 310 ft from home plate. The center fielder can throw the ball no harder than 110 ft/s. The runner tags up and runs for home plate.

Can the center fielder throw him out? To do so, he must get the ball to the catcher at an appropriate height before the runner can get to home plate.

If so, at what angle and what velocity does he need to throw the ball in order to put the runner out?

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Solving with Excel Open an Excel

Spreadsheet and create column heads like the example.

Rows 1 - 6 are for constants. Remember to use the $ notation when reference absolute address

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Solution - Using a Chart One way to solve this problem is

with a graphical representation. Generate data representing the

position of the ball (x(t) and y(t)) and the position of the runner (r(t)).

The next slide shows an example of a completed chart. Notice that the red line shows the ball’s position reaches 310 ft before the runner (blue line) has traveled 90 ft.

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