1 Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering
2 Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques (Looking at Graphs) Interpolation techniques Single and multiple algebraic equations Evaluating Integrals (Evaluate effects over time) Economic Analysis Optimization (Finding the best solution)
3 Applicable Engineering Fundamentals Most engineering problems are based upon one of three underlying principles: 1. Equilibrium Force, Flux, and Chemical 2. Conservation Laws Energy and Mass 3. Rate Phenomena How something changes over time.
4 What is a spreadsheet? A spreadsheet is basically a table containing NUMERICAL and/or ALPHANUMERICAL values. Individual elements are known as CELLS. Each CELL can contain a single value or a STRING (sequence of characters) The cells are arranged in columns and rows are referenced by a CELL ADDRESS ( For example, B3 refers to the cell in COLUMN B, row 3. The collection of cells is referred to as a WORKSHEET. A cell can have a manually entered number or be assigned a FORMULA EVALUATION such as C7 being =(C3+C4+C5)
5 The Excel Window
6 Entering Data There are two ways to enter data into Excel A simple numerical value called a number constant. A string, called a text constant. When you are finished entering a number in a cell hit ENTER or click the checkmark.
7 Using Formulas In Excel, a formula MUST always begin with an equal sign (=), followed by an expression involving: Consider: =(C3+B2+5) Constants C3 & B2 are cell addresses Operators 5 is the numerical constant Cell Addresses The (+) sign is the operator This formula could be entered in D7 where the formula would be applied. Note: Any change in C3 or B2 will automatically change D7!
9 Operator Preference Since some formulas include more than one operator, the question arises as to which one is carried out first. The order is outlined to the right. If any formula has two operators from the same group, the order is carried out from left to right. Operator Preference Operator 1 % 2 ^ 3 * and / 4 + and - For example, in the formula =(C1/D2*E3), the division would be carried out first then multiplication.
10 A Simple Spreadsheet Application A small machine shop has the following parts on hand: Item Quantity Screws 6500 Nuts 9000 Bolts 5400 Start by creating a worksheet that includes this information, plus the total number of parts on hand. Answer the questions on the worksheet provided.
11 Using Functions Excel includes many different functions which can carry out a wide variety of operations. They include: Mathematical and statistical operations Process financial data Process AND return text information Each function has a specific name followed by an ARGUMENT enclosed in parenthesis.
12 Function Examples =Sum(C1,C2,C3) This will add the numbers in the three cell addresses. The ARGUMENT is inside the parenthesis and separated by commas. =Sum(C1:C50) the use of a COLON indicates a RANGE and will add up ALL cells between the two cell addresses.
13 Other function examples =SQRT(x) Takes square root of x =Min(x1:x20) Returns the minimum # in the set =Max(x1:x20) Returns the maximum # in the set =Round (x,n) Rounds x to n decimal places =Average (x1:x15) Returns the average Example: =sum(a1, SQRT(A2/2),2*B3+5,D7:D12) This example has FOUR arguments as evidenced by the commas
14 Example #2 Student Exam Scores Create the following worksheet: See paper worksheet Student Exam 1 Exam 2 Final Exam Overall Score Davis Graham Jones Meyers Richards Thomas Williams
15 Moving things around! You can: Select and Highlight a block of cells Copy a block of cells Move a clock of cells Delete rows or columns Create grids Change font color, fill in backgrounds, etc Adjust column widths
16 Creating Graphs The easiest way to create a graph in Excel is to use the Chart Wizard! Follow these steps: Select the block of cells containing the data to be plotted. You may include headings! Click on the CHART WIZARD icon Choose the graph type Type in a title And select Chart on this worksheet or As object in
17 More on Graphs Graphs done on a SEPARATE sheet can easily be copied or pasted into a WORD document. Graphs embedded into worksheet can be edited even after they have been inserted.
18 Creating and Editing a Line Graph The voltage within an electronic device varies with time in accordance with the formula: V = 10e 0.5 Prepare an Excel worksheet and line graph (scatter) with the data to the right t Seconds Volts
19 Editing the graph Once the graph is embedded into the worksheet, click on the graph until the chart toolbox appears Select the drop down menu to add a title and label each axis with units. Also, choose LEGEND then RIGHT CLICK on the small box and choose CLEAR!
20 Analyzing Data Engineering analysis usually begins with the analysis of data! Engineers gather data to measure VARIABILITY or CONSISTENCY. Measured Data can tell you a great deal if you know how to interpret the results. Let Excel do the tedious work for you so that you can focus on the interpretation of results.
21 Data Characteristics There are several commonly used parameters that allow us to draw conclusions about the characteristics of a data set. They are: Mean Median Mode Max Min Variance Standard Deviation
22 Mean, Median, and Mode Mean is the arithmetic average of a data set. It represents expected behavior. AVERAGE( ) is used in Excel Median the value where half of the data falls above and half the data falls below. MEDIAN ( ) is used in Excel Mode the value that occurs with the greatest frequency with in data set. Mode ( ) is used in Excel. If a tie results it will always list the FIRST frequent number it encounters
23 Min and Max The min and Max simple represent the extremities of the data set. In Excel,the MIN ( ) and Max ( ) functions return these values. NOTE: The MIN and MAX functions return the values that are the smallest and largest ALGEBRAICALLY. They do not return values in terms of MAGNITUDE. Example: ( -5,-2, 1) ; Min = -5 & Max = 1
24 Variance The variance provides an indication of the degree of SPREAD in the data. The greater the variance, the greater the spread. It is determined by the following formula: Excel uses the VAR( ) function s s x 2 2 n = 1 ( x n 1 i = 1 = variance x = mean i x) n = # of data values i = individual data value 2
25 Standard Deviation The standard deviation is simply the square root of the variance. s = s 2 = standard deviation So why bother with the standard deviation? The variance is a much more practical value to have but its UNITS are NOT consistent with the mean, median, or mode. Excel use the stdev ( ) command.
26 Analyzing a data set A car manufacturer wishes to determine how accurately the cylinders are being machined in several engine blocks. The design specification call for a cylinder diameter of inches, with a tolerance of +/ inches. See paper worksheet
27 Histograms Thought the previous statistical characteristics can prove useful in interpreting data, it is often more desirable to the plot the data in a manner that illustrates how the values are distributed within their range. This is called a HISTOGRAM or RELATIVE FREQUENCY plot.
28 More on Histograms To create a histogram, you must first subdivide the range of the data into a series of adjacent, equally spaced intervals. The first interval must begin at or below the smallest value (the min) and the last interval must extend to or beyond the largest data value (the max). These intervals are called CLASS INTERVALS. Then you determine HOW MANY values fall within each interval
29 The car manufacturer continued The histogram feature is found under TOOLS then choose DATA ANALYSIS. The choose histogram. There are two things the histogram needs: An INPUT RANGE this comes from your data. Click on the Input range box then click on the first cell of the data, hold, and highlight until the last cell is chosen An OUTPUT RANGE this is the interval bounds. Do the same click and hold To see the chart you must click OUTPUT RANGE under OUTPUT OPTIONS and specify where you want the chart located. Click on the cell where you want it to be placed.
30 The car manufacturer continued Your histogram should look like this!
31 Relative Frequency Now we can go back and LOOK AT the percentage of values that fell into each interval. These values were found using the following equation: f f n n i i = = = = n i n relative frequency in the interval number of total number of values in that interval values in data set
32 Cumulative Distribution A histogram can provide a great graphical illustration of how a data set is distributed. A CUMULATIVE DISTRIBUTION is equally important. It provides us ANOTHER graphical way to view the data.but.it allows us to determine the LIKELIHOOD of a RANDOM VALUE being less than or greater than a specified value. It is almost like a percent chance and is the graphical representation of the calculated relative frequency.
33 Cumulative Distribution Cont To find the cumulative F = f distribution: 1 1 So basically you just sum up the relative frequency using the interval prior. F F 2 3 = = f f f f f 3... Create a cumulative distribution column using your relative frequency data.
34 Plotting the Cumulative Distribution Cut the original histogram and Choose TOOLS then data analysis. This time under OUTPUT OPTIONS click on cumulative distribution and chart output Notice that the calculated CD values will appear!
35 Fixing The Cumulative Distribution Plot The problem with this type of graph is that the bar graph has GAPS in it. Right Click on one of the bars in the graph Choose FORMAT DATA SERIES Click on OPTIONS Change GAP WIDTH to ZERO!
36 Drawing inferences A engineer can now look at the cumulative distribution and randomly pull a part off of the manufacturing line. The plot will tell him the % likelihood that an arbitrary cylinder diameter within a randomly selected engine block WILL NOT exceed a certain length. For example, what is the likelihood that a cylinder will NOT exceed inches?
37 Fitting Equations to Data The data an engineer collects could reveal: Spatial profile Time history Cause and effect relationship System output as a function of input Mathematical expressions are then used to CAPTURE the relationship shown in the data
38 Fitting a straight line to a set of data Data is usually represented by values that show some SCATTER, which is due to fluctuations or errors in measurement. Therefore, we NEVER connect the dots on a graph! We pass the points through an AGGREGATE or TRENDLINE. In science, this is probably referred to as a line of best fit.
39 Force exerted by a spring Data point # Distance (cm) Force (N)
40 Making a Trendline Using the data you just entered into EXCEL, use chart wizard to construct a SCATTER plot. Place in WORKSHEET 2. Add title and units to axes. RIGHT CLICK on one of the data points (all should highlight) and choose trendline. Since this plot looks linear, choose LINEAR. The choose OPTIONS and click on ADD equation to chart and ADD R value.
41 Regression Statistics Excel can also provide a great deal of built in statistics. But they may prove MORE than what you need. Choose TOOLS then DATA ANALYSIS Choose Regression Highlight the appropriate cells and where to place the stats.
42 Assessing Quality using r 2 The r 2 value helps and engineer assess the QUALITY of the curve fit. Any number close to 1.0 is a good fit. You can think of this value as a %fit. A 1.0 would represent 100%. If the r 2 value is too low, right click on the trendline and change the type to LOGARITHMIC or other type of curve fit. The largest r 2 value is the one that fits the data the best.
43 The OTHER fitting functions Exponential Logarithmic Power Function Polynomial ( NOTE: By INCREASING the order, you can increase your r 2 value)
Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data
EXCEL Tutorial: How to use EXCEL for Graphs and Calculations. Excel is powerful tool and can make your life easier if you are proficient in using it. You will need to use Excel to complete most of your
EXAMPLES - SAMPLING DISTRIBUTION EXCEL INSTRUCTIONS This exercise illustrates the process of the sampling distribution as stated in the Central Limit Theorem. Enter the actual data in Column A in MICROSOFT
FACT SHEET Using Excel for descriptive statistics Introduction Biologists no longer routinely plot graphs by hand or rely on calculators to carry out difficult and tedious statistical calculations. These
TIPS FOR DOING STATISTICS IN EXCEL Before you begin, make sure that you have the DATA ANALYSIS pack running on your machine. It comes with Excel. Here s how to check if you have it, and what to do if you
GeoGebra Statistics and Probability Project Maths Development Team 2013 www.projectmaths.ie Page 1 of 24 Index Activity Topic Page 1 Introduction GeoGebra Statistics 3 2 To calculate the Sum, Mean, Count,
Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.
Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships
SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing
Data exploration with Microsoft Excel: univariate analysis Contents 1 Introduction... 1 2 Exploring a variable s frequency distribution... 2 3 Calculating measures of central tendency... 16 4 Calculating
Calibration and Linear Regression Analysis: A Self-Guided Tutorial Part 1 Instrumental Analysis with Excel: The Basics CHM314 Instrumental Analysis Department of Chemistry, University of Toronto Dr. D.
Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool
Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using
A Guide to Using Excel in Physics Lab Excel has the potential to be a very useful program that will save you lots of time. Excel is especially useful for making repetitious calculations on large data sets.
Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application
CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES Microsoft Excel 2010 Part 3: Advanced Excel Winter 2015, Version 1.0 Table of Contents Introduction...2 Sorting Data...2 Sorting
Getting started in Excel Disclaimer: This guide is not complete. It is rather a chronicle of my attempts to start using Excel for data analysis. As I use a Mac with OS X, these directions may need to be
The Center for Teaching, Learning, & Technology Instructional Technology Workshops Microsoft Excel 2010 Formulas and Charts Albert Robinson / Delwar Sayeed Faculty and Staff Development Programs Colston
CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution
Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.
activity 17.1 Coins, Presidents, and Justices: Normal Distributions and z-scores In the first part of this activity, you will generate some data that should have an approximately normal (or bell-shaped)
INTRODUCTION TO EXCEL 1 INTRODUCTION Anyone who has used a computer for more than just playing games will be aware of spreadsheets A spreadsheet is a versatile computer program (package) that enables you
ESTIMATING THE DISTRIBUTION OF DEMAND USING BOUNDED SALES DATA Michael R. Middleton, McLaren School of Business, University of San Francisco 0 Fulton Street, San Francisco, CA -00 -- email@example.com
Spreadsheets and Laboratory Data Analysis: Excel 2003 Version (Excel 2007 is only slightly different) Spreadsheets are computer programs that allow the user to enter and manipulate numbers. They are capable
Dealing with Data in Excel 2010 Excel provides the ability to do computations and graphing of data. Here we provide the basics and some advanced capabilities available in Excel that are useful for dealing
8. Excel Charts and Analysis ToolPak Charts, also known as graphs, have been an integral part of spreadsheets since the early days of Lotus 1-2-3. Charting features have improved significantly over the
Experiment 0 Introduction to Data Analysis Using an Excel Spreadsheet I. Purpose The purpose of this introductory lab is to teach you a few basic things about how to use an EXCEL 2010 spreadsheet to do
Data exploration with Microsoft Excel: analysing more than one variable Contents 1 Introduction... 1 2 Comparing different groups or different variables... 2 3 Exploring the association between categorical
Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each
Formulas & Functions in Microsoft Excel Theresa A Scott, MS Biostatistician III Department of Biostatistics Vanderbilt University firstname.lastname@example.org Table of Contents 1 Introduction 1 1.1 Using
Microsoft Excel Qi Wei Excel (Microsoft Office Excel) is a spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot
Plots, Curve-Fitting, and Data Modeling in Microsoft Excel This handout offers some tips on making nice plots of data collected in your lab experiments, as well as instruction on how to use the built-in
business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel
Tutorial on Using Excel Solver to Analyze Spin-Lattice Relaxation Time Data In the measurement of the Spin-Lattice Relaxation time T 1, a 180 o pulse is followed after a delay time of t with a 90 o pulse,
Entering and Formatting Data Using Microsoft Excel to Plot and Analyze Kinetic Data Open Excel. Set up the spreadsheet page (Sheet 1) so that anyone who reads it will understand the page (Figure 1). Type
Microsoft Excel Tutorial by Dr. James E. Parks Department of Physics and Astronomy 401 Nielsen Physics Building The University of Tennessee Knoxville, Tennessee 37996-1200 Copyright August, 2000 by James
Running Descriptive and Correlational Analysis in Excel 2013 Tips for coding a survey Use short phrases for your data table headers to keep your worksheet neat, you can always edit the labels in tables
GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter
Statistics Revision Sheet Question 6 of Paper The Statistics question is concerned mainly with the following terms. The Mean and the Median and are two ways of measuring the average. sumof values no. of
Introduction to Statistical Computing in Microsoft Excel By Hector D. Flores; email@example.com, and Dr. J.A. Dobelman Statistics lab will be mainly focused on applying what you have learned in class with
Quickstart for Desktop Version What is GeoGebra? Dynamic Mathematics Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,
ETH Zürich Seminar für Statistik Introduction Course in SPSS - Evening 1 Seminar für Statistik, ETH Zürich All data used during the course can be downloaded from the following ftp server: ftp://stat.ethz.ch/u/sfs/spsskurs/
Page 1 Data representation and analysis in Excel Let s Get Started! This course will teach you how to analyze data and make charts in Excel so that the data may be represented in a visual way that reflects
Advanced Microsoft Excel 2010 Table of Contents THE PASTE SPECIAL FUNCTION... 2 Paste Special Options... 2 Using the Paste Special Function... 3 ORGANIZING DATA... 4 Multiple-Level Sorting... 4 Subtotaling
Volume 16, Number 4 - August 2000 to October 2000 Integrating Spreadsheet Templates and Data Analysis into Fluid Power Instruction By Dr. Bruce Marsh KEYWORD SEARCH Curriculum Fluid Power Teaching Methods
Formulas & Functions in Microsoft Excel Theresa A Scott, MS Biostatistician II Department of Biostatistics Vanderbilt University firstname.lastname@example.org Table of Contents 1 Introduction 1 1.1 Using
Microsoft Excel Tutorial Microsoft Excel spreadsheets are a powerful and easy to use tool to record, plot and analyze experimental data. Excel is commonly used by engineers to tackle sophisticated computations
KaleidaGraph Quick Start Guide This document is a hands-on guide that walks you through the use of KaleidaGraph. You will probably want to print this guide and then start your exploration of the product.
Formulas, Functions and Charts :: 167 8 Formulas, Functions and Charts 8.1 INTRODUCTION In this leson you can enter formula and functions and perform mathematical calcualtions. You will also be able to
COMMUNITY TECHNICAL SUPPORT Microsoft Excel Basics Introduction to Excel Click on the program icon in Launcher or the Microsoft Office Shortcut Bar. A worksheet is a grid, made up of columns, which are
AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks
Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.
Table of Contents TASK 1: DATA ANALYSIS TOOLPAK... 2 TASK 2: HISTOGRAMS... 5 TASK 3: ENTER MIDPOINT FORMULAS... 11 TASK 4: ADD TOTAL LABEL AND FORMULA FOR FREQUENCY... 12 TASK 5: MODIFICATIONS TO THE HISTOGRAM...
University of Wisconsin-Extension Cooperative Extension Madison, Wisconsin PD &E Program Development & Evaluation Using Excel for Analyzing Survey Questionnaires Jennifer Leahy G3658-14 Introduction You
Excel -- Creating Charts The saying goes, A picture is worth a thousand words, and so true. Professional looking charts give visual enhancement to your statistics, fiscal reports or presentation. Excel
Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.
Using Formulas, Functions, and Data Analysis Tools Excel 2010 Tutorial Excel file for use with this tutorial Tutor1Data.xlsx File Location http://faculty.ung.edu/kmelton/data/tutor1data.xlsx Introduction:
USING EXCEL ON THE COMPUTER TO FIND THE MEAN AND STANDARD DEVIATION AND TO DO LINEAR REGRESSION ANALYSIS AND GRAPHING Dr. Susan Petro TABLE OF CONTENTS Topic Page number 1. On following directions 2 2.
Using MS Excel to Analyze Data: A Tutorial Various data analysis tools are available and some of them are free. Because using data to improve assessment and instruction primarily involves descriptive and
Excel 2010: Create your first spreadsheet Goals: After completing this course you will be able to: Create a new spreadsheet. Add, subtract, multiply, and divide in a spreadsheet. Enter and format column
MBA 611 STATISTICS AND QUANTITATIVE METHODS Part I. Review of Basic Statistics (Chapters 1-11) A. Introduction (Chapter 1) Uncertainty: Decisions are often based on incomplete information from uncertain
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
Assignment objectives: Regression Pivot table Exercise #1- Simple Linear Regression Often the relationship between two variables, Y and X, can be adequately represented by a simple linear equation of the
MS EXCEL 2000 Spreadsheet Use, Formulas, Functions, References More than any other type of personal computer software, the spreadsheet has changed the way people do business. Spreadsheet software allows
SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet
Q&As: Microsoft Excel 2013: Chapter 2 In Step 5, why did the date that was entered change from 4/5/10 to 4/5/2010? When Excel recognizes that you entered a date in mm/dd/yy format, it automatically formats
1 Valor Christian High School Mrs. Bogar Biology Graphing Fun with a Paper Towel Lab I m sure you ve wondered about the absorbency of paper towel brands as you ve quickly tried to mop up spilled soda from
Common Tools for Displaying and Communicating Data for Process Improvement Packet includes: Tool Use Page # Box and Whisker Plot Check Sheet Control Chart Histogram Pareto Diagram Run Chart Scatter Plot
THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i
MARS STUDENT IMAGING PROJECT Data Analysis Practice Guide Mars Education Program Arizona State University Data Analysis Practice Guide This set of activities is designed to help you organize data you collect
For more info and downloads go to: http://school-maths.com Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It
Estimating a market model: Step-by-step Prepared by Pamela Peterson Drake Florida Atlantic University The purpose of this document is to guide you through the process of estimating a market model for the
Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor
Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing
Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course
Using Basic Formulas A formula can be a combination of values (numbers or cell references), math operators and expressions. Excel requires that every formula begin with an equal sign (=). Excel also has
Curve Fitting in Microsoft Excel By William Lee This document is here to guide you through the steps needed to do curve fitting in Microsoft Excel using the least-squares method. In mathematical equations
Updates to Graphing with Excel NCC has recently upgraded to a new version of the Microsoft Office suite of programs. As such, many of the directions in the Biology Student Handbook for how to graph with
1) Write the following as an algebraic expression using x as the variable: Triple a number subtracted from the number A. 3(x - x) B. x 3 x C. 3x - x D. x - 3x 2) Write the following as an algebraic expression
Bill Burton Albert Einstein College of Medicine email@example.com April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
Charting LibQUAL+(TM) Data Jeff Stark Training & Development Services Texas A&M University Libraries Texas A&M University Revised March 2004 The directions in this handout are written to be used with SPSS
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
Module gtf1 Simple Versus Compound Interest What is the difference between simple and compound interest and does it really matter? There are various methods for computing interest. Do you know what the
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREER-READY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical