Lab 1a: Experimental Uncertainties


 Harry Wade
 1 years ago
 Views:
Transcription
1 Physics 144 Chowdary How Things Work Spring 2006 Name: Partners Name(s): Lab 1a: Experimental Uncertainties Introduction Our first exploration today is intended to introduce you to the true nature of experimentation: no measurement is complete without some comment on the confidence with which it was measured. The key to doing experiments in any scientific field is making measurements. But when you make a measurement, there is always some uncertainty associated with it. Many times, these uncertainties are called experimental errors, but to me, that has always implied sloppiness. Of course, a good experimentalist will always seek to minimize the uncertainties in an experiment. But it is impossible ever to make a perfect measurement. In addition to minimizing errors, an experimentalist has to know how to determine the magnitude of the uncertainty. As we will see in this lab, knowing how large the uncertainty is in a measurement can be critical to making conclusions based on the data. In most of our everyday experience, the confidence that we have in our information is never explicitly stated. For instance, when asking someone what the temperature is outside, the response is always nearly a single number: It s 65 o today. This usually means that the true temperature outside is somewhere near 65 o, within a few degrees or so. The amount from which our measured value may be off from the actual value is called the experimental uncertainty or confidence limit of our measurement. When we hear that the temperature is 65o, we assume an uncertainty of a few degrees, and dress appropriately. Experience tells us that most times the temperature difference is rarely outside that range. You do often hear the confidence level given for polls. You probably expect to hear it. In fact, you should demand to hear it. And whenever you hear an experimental result obtained by measurement, you should demand to know the experimental uncertainty. The concepts and numerical tools illustrated in this lab have many applications in business (e.g., quality control and marketing surveys), politics (opinion polls), law (questions of evidence and proof), medicine (significance of changes in a patient's lab results), economics (measures of economic indicators), sociology (measurements of societal trends), etc. There are several goals of this lab: in particular, after finishing this lab, you should understand a) how measurement uncertainty can be reduced with the use of repeated measurements; b) how to characterize the magnitude of the uncertainty for a measured quantity; and c) how to make appropriate conclusions from your data, based on the uncertainty. Specifically, we ll develop the tools needed to answer the following question: How many brown M&M s would you expect to find in a typical bag? Later, you ll apply these tools to answer the following questions: Does the acceleration of an object sliding down a ramp depend on the mass of the object? Does the acceleration of an object sliding down a ramp depend on the angle of the ramp?
2 Instrumental Uncertainties vs. Statistical Uncertainties When you measure an object's length, you typically stick a ruler next to the object and read off the measurement from the ruler. There is some uncertainty in this measurement. First of all, the ruler only has markings down to a certain precision (say, a mark every millimeter), so your uncertainty is at least that amount. Second, there are frequently uncertainties associated with the fact that the scale may not be properly calibrated. For examples: if the ruler is bent, then the uncertainty might be even larger than the smallest increment on the ruler, or the end of the ruler might be worn down, so that zero isn t really zero. The same kinds of issues apply to weighing objects, timing intervals, etc. You can try to obtain a better ruler (or scale or watch), but you will still always have some minimum uncertainty associated with your measuring instrument. In many cases, uncertainties in measurements are due to random issues. For instance, if you are determining the duration of an event with a stopwatch, you might click the stopwatch on too early in some measurements and too late in other measurements. You might improve your timing method, say with practice or by using some form of automation via computer, but there will still be some uncertainty. The uncertainty due to this kind of random error cannot easily be estimated from a single measurement. If, on the other hand, you make several measurements, you can determine the uncertainty from the scatter in the individual measurements. Furthermore, if you average the individual measurements, you will get a value that is more accurate than any single measurement. That s why we try to make multiple measurements of some kinds of quantities, and apply the ideas of statistics to estimate the value and the uncertainty in the value. In this lab, we ll learn about statistical uncertainties. Procedure How many brown M&M s would you expect to find in a typical bag? Each person will be responsible for a particular bag of M&M s. Please don t eat your M&M s right away! (Don t worry, you ll get to eat them soon enough! And for those poor souls who don t like M&M s, your instructor will make the ultimate sacrifice and eat them for you ) 1) Open your bag and place the M&M s on a clean sheet of paper in front of you. Count the total number and the number of brown M&M s in your bag. Record your results below: Total Number of M&M s Number of Brown M&M s Question #1: Based on your sole measurement, what is your best estimate of the number of brown M&M s in a typical bag? Question #2: Based on your sole measurement, can you determine a confidence level for your answer to Question #1? Briefly explain. 2) Fill out a row on the table on the board for your results. When the table on the board is completed, copy the data to the following table:
3 Table 1: Class Results Name Total # # Brown It probably isn t surprising that both the Total # and # Brown might be different for each person. However, you should notice that the numbers are only slightly different. The real questions now are What is the best estimate for the number of Brown M&M s? How big is slightly? 3) There are lots of ways to present this information. One way is as in Table 1. Let s try a graphical way next. First, let s see how much variation there is in the individual measurements of the Brown M&M s: # Brown M&M's Student Number Graph 1: Variation in # Brown M&M s
4 4) Hopefully, from Graph 1 you notice that the # Brown seems to fluctuate about some value. It seems likely that that value would be a good estimate for the number of Brown M&M s in a typical bag. Question #3: What does that value seem to be, according to Graph 1? How could you calculate that value? What other common name would we give to that kind of calculation? Calculate this value using your calculator, and draw a dashed horizontal line representing this value on Graph 1. Please talk to your instructor. 5) So it seems to make sense that averaging together the number of Brown M&M s found in a number of different bags will give a good estimate for the number of Brown M&M s in a typical bag. However, to really know this number, we d need to measure the number of Brown M&M s in every bag ever created! Then, we could obtain the true mean. Of course, this is not practical (but it sure would be tasty), so we settle for looking at a subset of the overall number of bags. Obviously, the larger our subs et, the closer our experimental mean will be to the true mean. So we have our experimental average. However, we still haven t determined our confidence level: we don t know how much variation to expect in a single bag. Also, we don t know have a good estimate for how close our experimental mean is to the true mean. Luckily, these two estimates are closely linked. WARNING: Lots of people are confused by the distinction in the previous paragraph. We re actually trying to answer two questions, both related to the experimental mean: 1) In any given bag, by how many Brown M&M s do you expect to be off from the experimental mean? (i.e., for any single measurement, how far off do you expect that experimental result to be from the experimental mean). 2) How far away do you expect the experimental mean is from the true mean? Please ask your instructor if you don t understand these two questions. 6) From Graph 1, we get a sense of the variation in individual measurements from the experimental mean (which itself is our best estimate of the true mean). Now, we ll make another plot that shows this variation in a different way. We ll plot the number of times a particular number of Brown M&M s was found vs. that particular number. The number of times a particular number is found is called the frequency of that number. So for example, if there were 5 bags that had 16 Brown M&M s, the frequency of 16 would be 5. Here s an example: let s say we found 3 bags with 12 M&M s; 4 bags with 15 M&M s; 5 bags with 16 M&M s; and 3 bags with 17 M&M s. I d make a table with two columns: the first column would be a particular measurement (here the number of M&M s in a bag) and the second column would be the frequency of that measurement (here the number of bags with that number of M&M s). Then I d plot the first column on the horizontal axis and the second column on the vertical axis. I find it easy to use X s. This kind of a plot is called a frequency distribution plot or a histogram. You have almost certainly seen this when teachers report how students did on an exam.
5 Table 2: Example Frequency Distribution Table Graph 2: Example Histogram # of Brown M&M s Frequency X 13 0 X X 14 0 X X X X 15 4 X X X X 16 5 X X X X Please ask if you re unsure what s going on with a histogram. 7) Now, make a histogram of the class data as on the board or in your Table 1. I ve provided some axes below, but you ll need to fill in the numbers on the horizontal axis. Also, make sure you label the horizontal axis. Finally, draw a dashed vertical line for your experimental mean. Graph 3: Histogram of class data for # Brown M&M s 8) Both Graph 1 and Graph 3 tell us information about the spread in the experimental mean. In other words, they graphically represent the uncertainty in that measurement. To calculate a number that corresponds to that spread, we ll look at the spread of each individual result. We ll consider the spread of each individual result to be how far away each individual result is from the average. In Table 3, copy the appropriate data from Table 1, and also fill in the values for Column 3, labeled # Brown Average. 9) You ll notice that some of the values you just calculated in step 8 are positive, and some are negative. This makes sense, as the average is somewhere in the middle of the individual results. However, this means that we can t just average together the individual spreads. Instead, we ll get rid of the negative sign by squaring. So Column 4 is Column 3, squared. Then, we ll take the average. And then, we ll take the square root (to make up for squaring before). That might seem a little complicated, but just follow along with the table, and as the last step, take the square root of the shaded box. Please ask your instructor to check your work.
6 Column 1 Column 2 Column 3 Column 4 # Brown # Brown Average (# Brown Average) Average Table 3: Calculating the Uncertainty. 10) The square root of the number in the shaded box is known as the standard deviation. This is the best estimate of the spread in the class results, and tells you the confidence level that you have: for any single bag, there is a 68% chance that the number of Brown M&M s will fall within the range between the experimental mean the standard deviation and the experimental mean + the standard deviation. (Actually, this 68% is only true if the histogram is a bellshaped curve, known more formally as a Gaussian. Our calculation of the standard deviation is still correct, and it is still a good indicator of the confidence level; it s just that we might not be able to say 68%.) On Graph 3, draw a dashed vertical line representing the experimental mean the standard deviation and the experimental mean + the standard deviation. Note that some of our measurements fall outside this range. As mentioned above, this range tells us where to expect to find 68% of all M&M bags. If we wanted to know the range in which 95% of the measurements would fall, we d double the standard deviation. And if we wanted to be even more certain, a range of 3 standard deviations to either side of the experimental mean would include 99.7% of all possible results! 11) However, this only answers half our questions. We ve identified the experimental mean along with the standard deviation. This answers the first question: In any given bag, by how many Brown M&M s do you expect to be off from the experimental mean? (i.e., for any single measurement, how far off do you expect that experimental result to be from the experimental mean). What about the second question: How far away do you expect the experimental mean is from the true mean? Well, it turns out to be fairly straightforward, given that we ve already calculated the standard deviation. The quantity of interest that we want is called the standard deviation of the mean, and is given by the standard deviation divided by the square root of the number of measurements that were made. This makes some sense: the more measurements you make, the closer your experimental mean should be to the true mean. So the standard deviation of the mean = standard deviation number of measurements And you expect the true mean to be within one standard deviation of the mean of the experimental average.
7 12) Determine the standard deviation of the mean. Conclusions We ve learned that making multiple measurements of the same quantity gives a better estimate than a single measurement. Averaging together multiple measurements to get the experimental mean gives an estimate of the true mean. We ve seen several ways to represent the spread in measurements, via graphs and calculation. We re confident that any single measurement lies in the range: experiment al mean ± standard deviation. We re confident that the true mean lies in the range: experiment al mean ± standard deviation of the mean Questions a) Your instructor is about to open up a bag of M&M s. Write down your best estimate for the number of Brown M&M s your instructor will find. b) The other lab section does the same lab as your half, and determines that their true mean lies in the range 9 ± 3. Might it reasonable to conclude that their bags came from a different case than your lab section s bags?
8 Lab 1b: Graphing Motion Introduction Our second activity today will give you practice with the connection between position, velocity, and acceleration. You ll get exposure to graphing motion curves (position vs. time, velocity vs. time, and acceleration vs. time). You ll use a computer and an ultrasonic motion detector to generate motion curves. You ll use the techniques you develop here in the next section of today s lab activities. All the motion in this section is onedimensional. We ve seen onedimensional motion in the path of a ball as it travels up and down when thrown straight up. Here, we ll look at it for a cart on a low friction track as it moves back and forth. Position vs. Time At your lab station is a cart on a low friction track. You can see that you can roll the cart back and forth along the track. The track is marked with a ruler, so you can measure the position of the cart. Below is a proposed position vs. time graph for the cart moving back and forth. position time 1) With your partner(s), determine how you would have to move the cart along the track in order to get this position vs. time graph. When/where would you not be moving? When would you be moving fast or slow? When would you be moving to the left or to the right? Briefly describe how you would move the cart to get the position vs. time graph shown.
9 2) On the axes below, sketch the velocity vs. time curve that corresponds to the position vs. time curve above. Some things to consider: a) On the position vs. time graph, were there any times when the velocity was zero? How did you know? Draw those first. b) On the position vs. time graph, weere there any times when the velocity was constant? Here s how you could check: for constant velocity, the acceleration is zero. Zero acceleration is constant acceleration, so we 1 2 can use eq. (1.2.3): x = x0 + v0 t + 2 a t. What does this become for a = 0? That should look like the equation of a straight line. So a straight line on a position vs. time graph means constant velocity. The steeper the slope, the faster it moves. That makes sense, since a steep slope means a larger change in position. We can go one step further: if part of a position vs. time graph is curved, the velocity isn t constant; in other words there s an acceleration! c) How about positive velocity vs. negative velocity? Well, positive velocity means that the cart is moving in the positive direction, and negative velocity means that the cart is moving in the negative direction. d) Put that together and draw the sketch below. There aren t any numbers, but it should show zero, positive, negative; large vs. small, constant vs. non constant. velocity time 3) Are there any times when the acceleration is NOT zero? Mark those points on the curve above with arrows. If the acceleration is positive (here that means the cart is speeding up), mark it with a plus sign. If the acceleration is negative, mark it with a minus sign. Note that you can t really have abrupt changes like we re showing here. Some things to note: Velocity is the slope of a position vs. time graph Acceleration is the slope of a velocity vs. time graph
10 Graphing Motion with LabPro At your lab bench, you should see a green box labeled LabPro. This is an interface that uses various sensors to collect data and sends the data directly to the computer, where it can be analyzed in a variety of ways. You should see that the LabPro unit is connected to a rectangular blue box with a gold screen on it (the Motion Detector). The Motion Detector is mounted on a stand at one end of the ramp. The Motion Detector works on the same principle as the echolocation used by bats to hunt insects and avoid midair collisions, except the Motion Detector use sound waves, while bats likely use some complicated combination of senses. Basically, the Motion Detector sends out a sound wave, and the sound wave bounces off nearby objects, returning to the Motion Detector. The time between the sound wave being emitted and then being detected can be used to determine the position of the nearby object. In this way, the Motion Detector can create a position vs. time graph. Then, by using the slope argument we talked about earlier, the computer can create velocity vs. time and acceleration vs. time graphs as well. Procedure 1) Turn on the power to the LabPro unit by turning on the power to the power strip on the table. Log onto the computer. On the desktop is a folder called PHYS141. Open that folder, and then open the folder named Phys144. You should see an icon named Lab #1.MBL; doubleclick that icon to launch a data collection program called LoggerPro. You might get some initialization messages; just click Scan, then OK. 2) You should see a graph open up, with Distance on the vertical axis and Time on the horizontal axis, just like the position vs. time graphs we worked with earlier. You ll notice that the Distance axis goes from 1.5 to 1.5, but we can t actually get to less than zero since that would be the other side of the Motion Detector, which only works in one direction! Also, due to limitations on the machine, it doesn t work well for distances less than 50 cm from the detector. So make sure you limit the motion of the cart to between 50 cm from the detector and 1.5 m from the detector. 3) Position the cart approximately 70 cm from the detector. Note that the detector isn t set all the way at one end, so you need to be careful using the ruler on the track. Hold the cart fixed, and hit Enter on the keyboard. You should here the Motion Detector emitting a rapid clicking noise. The program collects data for 10 seconds; move the cart back and forth and you should see the position vs. time graph appear on the screen. 4) Now, as best you can, follow your description of how to move the cart to get the position vs. time graph you worked with earlier. It doesn t have to be perfect, but I would like to see a flat line, a steep positiveslope line, a shallow negativeslope line, and another flat line. Play around until you get something you like, and then call me over to look at it. 5) Looking at your position vs. time graph, what do you think the velocity vs. time graph will look like? You can make the computer plot velocity vs. time for you. Go to View, then Graph Options, then Axis Options, and on Vertical axis, click Velocity and hit OK. Does the velocity vs. time graph look like you d expect? Note that there may be some funny points. There are two reasons: the Motion Detector isn t perfect, and you might have noticed some funny bumps and wiggles in the position vs. time curve. So that will give some problems. Also, the slope calculation can t be perfect either. However, most of the results should seem quite reasonable to you. 6) Now, looking at your velocity vs. time graph, what do you think acceleration vs. time will look like? Again, you can make the computer plot this for you as well, following the same procedure as above. What does this graph look like? 7) Go back and remove the velocity and acceleration parts from the graph, leaving just distance vs. time.
11 Lab 1c: Motion on Ramps Introduction Our final activity today will have you collect data using the Motion Detector and analyze it using the techniques we developed for statistical uncertainties. We ll want to answer the following 2 questions to the best of our abilities, experimentally. Does the acceleration of an object sliding down a ramp depend on the mass of the object? Does the acceleration of an object sliding down a ramp depend on the angle of the ramp? Half the lab section will try to answer the first question, and half the lab section will try to answer the other; you ll share your results with another group in your lab section. Procedure (same for both questions) 1) Use the wooden block carefully to prop up the end of the ramp away from the motion detector. Maintain the general direction of the ramp. Prop it up using the short dimension of the block. 2) It turns out that you ll get better data if you start the cart low on the track, give it a push up and let it coast to its highest position and then coast back. Please don t let the cart bang into either end of the ramp; stop it with your hands if necessary. Try it a couple of times until you get good data; it should look something like this: Please show me your graph before proceeding. 3) Now, show velocity on your curve. Hopefully the velocity vs. time graph is linear in the region of interest (as we d expect for constant acceleration), and we can obtain the acceleration by getting the slope of the velocity vs. time graph. Ask your instructor how to get the slope, and write it down. 4) Repeat the experiment until you have at least 5 values for the acceleration of the cart. Write down your experimentally determined values for the acceleration of the cart.
12 5) At this point, your instructor should have told you which question you re going to answer. Perform your second experiment. Make sure you obtain and write down at least 5 values of acceleration. 6) Now, using the statistical tools we developed earlier, determine the experimental mean, the standard deviation, and the standard deviation of the mean for the acceleration of your two cases (your group and your partner group). Write down the experiment al mean ± standard deviation of the mean for each case. Do they overlap? If they do overlap, what can you conclude about the acceleration for your two cases? If they don t overlap, by how much are they apart? What can you conclude in this case? Please discuss your conclusions with your instructor, and turn in your lab packet.
AP Physics 1 and 2 Lab Investigations
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
More informationISA HELP BOOKLET AQA SCIENCE NAME: Class:
ISA HELP BOOKLET AQA SCIENCE NAME: Class: Controlled Assessments: The ISA This assessment is worth 34 marks in total and consists of three parts: A practical investigation and 2 written test papers. It
More informationMotion Graphs. It is said that a picture is worth a thousand words. The same can be said for a graph.
Motion Graphs It is said that a picture is worth a thousand words. The same can be said for a graph. Once you learn to read the graphs of the motion of objects, you can tell at a glance if the object in
More informationEXPERIMENTAL ERROR AND DATA ANALYSIS
EXPERIMENTAL ERROR AND DATA ANALYSIS 1. INTRODUCTION: Laboratory experiments involve taking measurements of physical quantities. No measurement of any physical quantity is ever perfectly accurate, except
More informationMicrosoft Excel Tutorial
Microsoft Excel Tutorial by Dr. James E. Parks Department of Physics and Astronomy 401 Nielsen Physics Building The University of Tennessee Knoxville, Tennessee 379961200 Copyright August, 2000 by James
More informationA Guide to Using Excel in Physics Lab
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.
More informationUsing Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data
Using Excel (Microsoft Office 2007 Version) for Graphical Analysis of Data Introduction In several upcoming labs, a primary goal will be to determine the mathematical relationship between two variable
More information0 Introduction to Data Analysis Using an Excel Spreadsheet
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
More information2After completing this chapter you should be able to
After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time
More informationHow To Run Statistical Tests in Excel
How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D
ART 269 3D Animation Fundamental Animation Principles and Procedures in Cinema 4D Components Tracks An animation track is a recording of a particular type of animation; for example, rotation. Some tracks
More informationEngineering Problem Solving and Excel. EGN 1006 Introduction to Engineering
Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques
More informationAt the skate park on the ramp
At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises
More informationSTB 2. Installation and Operation Manual
STB 2 Installation and Operation Manual Index 1 Unpacking your STB 2 2 Installation 3 WIFI connectivity 4 Remote Control 5 Selecting Video Mode 6 Start Page 7 Watching TV / TV Guide 8 Recording & Playing
More informationData Acquisition And Analysis
Data Acquisition And Analysis Objective: To gain familiarity with some of the measurement tools you will use in lab this semester. To learn how to measure distance with a motion sensor and force with a
More informationPhysics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics  Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More information21 Position, Displacement, and Distance
21 Position, Displacement, and Distance In describing an object s motion, we should first talk about position where is the object? A position is a vector because it has both a magnitude and a direction:
More informationData representation and analysis in Excel
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
More informationDESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.
DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,
More information1.3.1 Position, Distance and Displacement
In the previous section, you have come across many examples of motion. You have learnt that to describe the motion of an object we must know its position at different points of time. The position of an
More information1.2 Investigations and Experiments
Science is about figuring out cause and effect relationships. If we do something, what happens? If we make a ramp steeper, how much faster will a car roll down? This is an easy question. However, the process
More informationFree Fall: Observing and Analyzing the Free Fall Motion of a Bouncing PingPong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)
Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing PingPong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure
More informationAP * Statistics Review. Descriptive Statistics
AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production
More informationAugmented reality enhances learning at Manchester School of Medicine
Augmented reality enhances learning at Manchester School of Medicine Welcome to the Jisc podcast. The University of Manchester is taking a unique approach to prescription training for its medical students
More informationManaging Your Class. Managing Users
13 Managing Your Class Now that we ve covered all the learning tools in Moodle, we ll look at some of the administrative functions that are necessary to keep your course and students organized. This chapter
More informationINTRODUCTION TO ERRORS AND ERROR ANALYSIS
INTRODUCTION TO ERRORS AND ERROR ANALYSIS To many students and to the public in general, an error is something they have done wrong. However, in science, the word error means the uncertainty which accompanies
More informationLab 11. Simulations. The Concept
Lab 11 Simulations In this lab you ll learn how to create simulations to provide approximate answers to probability questions. We ll make use of a particular kind of structure, called a box model, that
More information8. THE NORMAL DISTRIBUTION
8. THE NORMAL DISTRIBUTION The normal distribution with mean μ and variance σ 2 has the following density function: The normal distribution is sometimes called a Gaussian Distribution, after its inventor,
More informationOperations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras
Operations and Supply Chain Management Prof. G. Srinivasan Department of Management Studies Indian Institute of Technology Madras Lecture  41 Value of Information In this lecture, we look at the Value
More informationFormulas, Functions and Charts
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
More informationLESSON 7: IMPORTING AND VECTORIZING A BITMAP IMAGE
LESSON 7: IMPORTING AND VECTORIZING A BITMAP IMAGE In this lesson we ll learn how to import a bitmap logo, transform it into a vector and perform some editing on the vector to clean it up. The concepts
More information1 of 7 9/5/2009 6:12 PM
1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]
More informationNCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )
Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates
More informationHello Purr. What You ll Learn
Chapter 1 Hello Purr This chapter gets you started building apps. It presents the key elements of App Inventor the Component Designer and the Blocks Editor and leads you through the basic steps of creating
More informationSimple Linear Regression
STAT 101 Dr. Kari Lock Morgan Simple Linear Regression SECTIONS 9.3 Confidence and prediction intervals (9.3) Conditions for inference (9.1) Want More Stats??? If you have enjoyed learning how to analyze
More informationINTRUSION PREVENTION AND EXPERT SYSTEMS
INTRUSION PREVENTION AND EXPERT SYSTEMS By Avi Chesla avic@vsecure.com Introduction Over the past few years, the market has developed new expectations from the security industry, especially from the intrusion
More informationGetting Started in Tinkercad
Getting Started in Tinkercad By Bonnie Roskes, 3DVinci Tinkercad is a fun, easy to use, webbased 3D design application. You don t need any design experience  Tinkercad can be used by anyone. In fact,
More informationMATH 140 Lab 4: Probability and the Standard Normal Distribution
MATH 140 Lab 4: Probability and the Standard Normal Distribution Problem 1. Flipping a Coin Problem In this problem, we want to simualte the process of flipping a fair coin 1000 times. Note that the outcomes
More informationSpreadsheets and Laboratory Data Analysis: Excel 2003 Version (Excel 2007 is only slightly different)
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
More informationA Sales Strategy to Increase Function Bookings
A Sales Strategy to Increase Function Bookings It s Time to Start Selling Again! It s time to take on a sales oriented focus for the bowling business. Why? Most bowling centres have lost the art and the
More informationPlots, CurveFitting, and Data Modeling in Microsoft Excel
Plots, CurveFitting, 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 builtin
More informationA Quick Algebra Review
1. Simplifying Epressions. Solving Equations 3. Problem Solving 4. Inequalities 5. Absolute Values 6. Linear Equations 7. Systems of Equations 8. Laws of Eponents 9. Quadratics 10. Rationals 11. Radicals
More informationITS Training Class Charts and PivotTables Using Excel 2007
When you have a large amount of data and you need to get summary information and graph it, the PivotTable and PivotChart tools in Microsoft Excel will be the answer. The data does not need to be in one
More informationUSER MANUAL (PROCURO LITE, PRO & ENT) [SUPPLIED FOR VERSION 3]
Procuro Software Ltd USER MANUAL (PROCURO LITE, PRO & ENT) [SUPPLIED FOR VERSION 3] CONTENTS Everyday use... 3 Logging on... 4 Main Screen... 5 Adding locations... 6 Working with locations... 7 Duplicate...
More informationT O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these
More informationREPORT WRITING GUIDE
Report Writing Guide F2009 1 REPORT WRITING GUIDE Introduction The importance of good report writing and data presentation cannot be overemphasized. No matter how good an experiment, or how brilliant a
More informationGas Dynamics Prof. T. M. Muruganandam Department of Aerospace Engineering Indian Institute of Technology, Madras. Module No  12 Lecture No  25
(Refer Slide Time: 00:22) Gas Dynamics Prof. T. M. Muruganandam Department of Aerospace Engineering Indian Institute of Technology, Madras Module No  12 Lecture No  25 PrandtlMeyer Function, Numerical
More informationHerzog Keyboarding Grades 3 through 5. Overarching Essential Questions
Herzog Keyboarding Grades 3 through 5 Overarching Essential Questions How will learning to keyboard help me with my academics today and my career tomorrow? Introduction The lessons in the Herzog Keyboarding
More informationChapter 7: Momentum and Impulse
Chapter 7: Momentum and Impulse 1. When a baseball bat hits the ball, the impulse delivered to the ball is increased by A. follow through on the swing. B. rapidly stopping the bat after impact. C. letting
More informationTHE STATISTICAL TREATMENT OF EXPERIMENTAL DATA 1
THE STATISTICAL TREATMET OF EXPERIMETAL DATA Introduction The subject of statistical data analysis is regarded as crucial by most scientists, since errorfree measurement is impossible in virtually all
More informationLinear Equations. 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber
Linear Equations 5 Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI 83
More informationTutorial 1: The Freehand Tools
UNC Charlotte Tutorial 1: The Freehand Tools In this tutorial you ll learn how to draw and construct geometric figures using Sketchpad s freehand construction tools. You ll also learn how to undo your
More informationAssignment 2: Animated Transitions Due: Oct 12 Mon, 11:59pm, 2015 (midnight)
1 Assignment 2: Animated Transitions Due: Oct 12 Mon, 11:59pm, 2015 (midnight) Overview One of the things that make a visualization look polished is to add animation (animated transition) between each
More information8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight
1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled
More informationIf A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C?
Problem 3 If A is divided by B the result is 2/3. If B is divided by C the result is 4/7. What is the result if A is divided by C? Suggested Questions to ask students about Problem 3 The key to this question
More informationCSC 120: Computer Science for the Sciences (R section)
CSC 120: Computer Science for the Sciences (R section) Radford M. Neal, University of Toronto, 2015 http://www.cs.utoronto.ca/ radford/csc120/ Week 2 Typing Stuff into R Can be Good... You can learn a
More informationDVR GUIDE. Using your DVR/MultiRoom DVR. 1866WAVE123 wavebroadband.com
DVR GUIDE Using your DVR/MultiRoom DVR 1866WAVE123 wavebroadband.com Table of Contents Control Live TV... 4 Playback Controls... 5 Remote Control Arrow Buttons... 5 Status Bar... 5 Pause... 6 Rewind...
More informationThe BulletBlock Mystery
LivePhoto IVV Physics Activity 1 Name: Date: 1. Introduction The BulletBlock Mystery Suppose a vertically mounted 22 Gauge rifle fires a bullet upwards into a block of wood (shown in Fig. 1a). If the
More informationCorrecting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners
Correcting the Lateral Response Artifact in Radiochromic Film Images from Flatbed Scanners Background The lateral response artifact (LRA) in radiochromic film images from flatbed scanners was first pointed
More informationEDUH 1017  SPORTS MECHANICS
4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH 1017  SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use
More informationPERSONAL LEARNING PLAN STUDENT GUIDE
PERSONAL LEARNING PLAN STUDENT GUIDE TABLE OF CONTENTS SECTION 1: GETTING STARTED WITH PERSONAL LEARNING STEP 1: REGISTERING FOR CONNECT P.2 STEP 2: LOCATING AND ACCESSING YOUR PERSONAL LEARNING ASSIGNMENT
More information(I) s(t) = s 0 v 0 (t t 0 ) + 1 2 a (t t 0) 2 (II). t 2 = t 0 + 2 v 0. At the time. E kin = 1 2 m v2 = 1 2 m (a (t t 0) v 0 ) 2
Mechanics Translational motions of a mass point Onedimensional motions on the linear air track LD Physics Leaflets P1.3.3.8 Uniformly accelerated motion with reversal of direction Recording and evaluating
More informationDrawing a histogram using Excel
Drawing a histogram using Excel STEP 1: Examine the data to decide how many class intervals you need and what the class boundaries should be. (In an assignment you may be told what class boundaries to
More information6th Grade Lesson Plan: Probably Probability
6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use
More informationExercise 1: How to Record and Present Your Data Graphically Using Excel Dr. Chris Paradise, edited by Steven J. Price
Biology 1 Exercise 1: How to Record and Present Your Data Graphically Using Excel Dr. Chris Paradise, edited by Steven J. Price Introduction In this world of high technology and information overload scientists
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationMailing lists process, creation and approval. Mailing lists process, creation and approval
Mailing lists process, creation and approval Steps to creating your mailing list 1. Establish whether there is a generic mailing list that can be used (i.e. a list a sector or team use for every mailing)
More informationWhy Your Business Needs a Website: Ten Reasons. Contact Us: 727.542.3592 Info@intensiveonlinemarketers.com
Why Your Business Needs a Website: Ten Reasons Contact Us: 727.542.3592 Info@intensiveonlinemarketers.com Reason 1: Does Your Competition Have a Website? As the owner of a small business, you understand
More informationCREATIVE S SKETCHBOOK
Session Plan for Creative Directors CREATIVE S SKETCHBOOK THIS SKETCHBOOK BELONGS TO: @OfficialSYP 1 WELCOME YOUNG CREATIVE If you re reading this, it means you ve accepted the WeCTV challenge and are
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationEncoded Phased Array Bridge Pin Inspection
Encoded Phased Array Bridge Pin Inspection James S. Doyle Baker Testing Services, Inc. 22 Reservoir Park Dr. Rockland, MA 02370 (781) 8714458; fax (781) 8710123; email jdoyle@bakertesting.com Product
More informationc. Construct a boxplot for the data. Write a one sentence interpretation of your graph.
MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than nonsmokers. Does this imply that smoking causes depression?
More informationMicrosoft Word defaults to left justified (aligned) paragraphs. This means that new lines automatically line up with the left margin.
Microsoft Word Part 2 Office 2007 Microsoft Word 2007 Part 2 Alignment Microsoft Word defaults to left justified (aligned) paragraphs. This means that new lines automatically line up with the left margin.
More informationProtocol for Leaf Image Analysis Surface Area
Protocol for Leaf Image Analysis Surface Area By Kitren Glozer Associate Project Scientist Dept. of Plant Sciences, University of California, Davis Contact information: Dept. of Plant Sciences, University
More informationFREQUENCY RESPONSE OF AN AUDIO AMPLIFIER
2014 Amplifier  1 FREQUENCY RESPONSE OF AN AUDIO AMPLIFIER The objectives of this experiment are: To understand the concept of HIFI audio equipment To generate a frequency response curve for an audio
More informationUsing Excel for descriptive statistics
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
More informationWaveforms and the Speed of Sound
Laboratory 3 Seth M. Foreman February 24, 2015 Waveforms and the Speed of Sound 1 Objectives The objectives of this excercise are: to measure the speed of sound in air to record and analyze waveforms of
More informationUnit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas:
Unit #3: Investigating Quadratics (9 days + 1 jazz day + 1 summative evaluation day) BIG Ideas: Developing strategies for determining the zeroes of quadratic functions Making connections between the meaning
More informationLEARNING LAB WORKBOOK
LEARNING LAB WORKBOOK DOCLLW Version 1 Copyright 2004, 2005 by Steven Dworkin, Ph.D and Med Associates Inc. All rights reserved. Published by Med Associates Inc., P.O. Box 319, St. Albans, Vermont 05478
More informationPhysics 40 Lab 1: Tests of Newton s Second Law
Physics 40 Lab 1: Tests of Newton s Second Law January 28 th, 2008, Section 2 Lynda Williams Lab Partners: Madonna, Hilary Clinton & Angie Jolie Abstract Our primary objective was to test the validity
More informationAnalytical Test Method Validation Report Template
Analytical Test Method Validation Report Template 1. Purpose The purpose of this Validation Summary Report is to summarize the finding of the validation of test method Determination of, following Validation
More informationUnderstanding barcodes. www.brightpearl.com. White paper
White paper Understanding barcodes. Barcodes turn manual product lookups into an automated process that s efficient and virtually errorfree. In this white paper, you ll learn what they are, when to use
More informationScience Notebooks in the Classroom. Notebook Criteria
presentapresents Presents Science Notebooks in the Classroom kdkrifr Notebook Criteria This document was developed by Bay Area Schools for Excellence in Education (BASEE) a local systemic change project
More informationThe Viscosity of Fluids
Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et
More informationWhy are thesis proposals necessary? The Purpose of having thesis proposals is threefold. First, it is to ensure that you are prepared to undertake the
Guidelines for writing a successful MSc Thesis Proposal Prof. Dr. Afaf ElAnsary Biochemistry department King Saud University Why are thesis proposals necessary? The Purpose of having thesis proposals
More informationStudent Applications Help
Student Applications Help Understanding your Student Landing Page When you log into YES, Your Enrollment Services, you will enter the student landing page. This page will launch you to your academic applications.
More informationBuilding Qualtrics Surveys for EFS & ALC Course Evaluations: Step by Step Instructions
Building Qualtrics Surveys for EFS & ALC Course Evaluations: Step by Step Instructions Jennifer DeSantis August 28, 2013 A relatively quick guide with detailed explanations of each step. It s recommended
More informationPolynomial Degree and Finite Differences
CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial
More informationMAIL MERGE MADE EASY A STEPBYSTEP GUIDE FOR LABELS OR EMAIL MERGES
MAIL MERGE MADE EASY A STEPBYSTEP GUIDE FOR LABELS OR EMAIL MERGES WHY MAIL MERGE? Labels: Mail merge in Office lets you convert your contact list data into a sheet of mailing labels, with complete control
More informationUsing Microsoft Access
Using Microsoft Access Relational Queries Creating a query can be a little different when there is more than one table involved. First of all, if you want to create a query that makes use of more than
More informationInteractive Logging with FlukeView Forms
FlukeView Forms Technical Note Fluke developed an Event Logging function allowing the Fluke 89IV and the Fluke 189 models to profile the behavior of a signal over time without requiring a great deal of
More informationReview Assessment: Lec 02 Quiz
COURSES > PHYSICS GUEST SITE > CONTROL PANEL > 1ST SEM. QUIZZES > REVIEW ASSESSMENT: LEC 02 QUIZ Review Assessment: Lec 02 Quiz Name: Status : Score: Instructions: Lec 02 Quiz Completed 20 out of 100 points
More informationLecture 6. Weight. Tension. Normal Force. Static Friction. Cutnell+Johnson: 4.84.12, second half of section 4.7
Lecture 6 Weight Tension Normal Force Static Friction Cutnell+Johnson: 4.84.12, second half of section 4.7 In this lecture, I m going to discuss four different kinds of forces: weight, tension, the normal
More informationMSc in Autonomous Robotics Engineering University of York
MSc in Autonomous Robotics Engineering University of York Practical Robotics Module 2015 A Mobile Robot Navigation System: Labs 1a, 1b, 2a, 2b. Associated lectures: Lecture 1 and lecture 2, given by Nick
More informationThe electrical field produces a force that acts
Physics Equipotential Lines and Electric Fields Plotting the Electric Field MATERIALS AND RESOURCES ABOUT THIS LESSON EACH GROUP 5 alligator clip leads 2 batteries, 9 V 2 binder clips, large computer LabQuest
More informationAppendix C. Vernier Tutorial
C1. Vernier Tutorial Introduction: In this lab course, you will collect, analyze and interpret data. The purpose of this tutorial is to teach you how to use the Vernier System to collect and transfer
More information2013 MBA Jump Start Program
2013 MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Algebra Review Calculus Permutations and Combinations [Online Appendix: Basic Mathematical Concepts] 2 1 Equation of
More informationStarting Your Fee Based Financial Planning Practice From Scratch (Part 2) FEE008
Starting Your Fee Based Financial Planning Practice From Scratch (Part 2) FEE008 Episode Transcript Host: Scott Plaskett, CFP Okay. So let s get onto the feature segment. And this is a continuation from
More informationSMART board 101. SMART board 101 Training
SMART board 101 SMART board 101 Training For those who want to learn/remember how to connect it, turn it on, configure it, and feel better about using it at a basic level. We will talk about how the SMART
More information