WindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12

Save this PDF as:

Size: px
Start display at page:

Download "WindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12"

Transcription

1 WidWise Educatio T rasformig the Eergy of Wid ito Powerful Mids A Curriculum for Grades 6 12 Notice Except for educatioal use by a idividual teacher i a classroom settig this work may ot be reproduced or distributed by mechaical or by electroic meas without writte permissio from KidWid or Normadeau. For permissio to copy portios or all of this material for other purposes, such as for iclusio i other documets, please cotact Michael Arqui at the KidWid Project at 2 d editi o

2 WidWise Educatio was developed with fudig from the New York State Eergy Research & Developmet Authority Updates to Lessos 3 & 5 ad the additio of Lesso 16 were fuded by the Departmet of Eergy: subcotract No. AFT V2.0

3 TURBINES LESSON 10 WHICH BLADES ARE BEST? KEY CONCEPT Studets lear through experimetatio how differet blade desigs are more efficiet at haressig the eergy of the wid. TIME REQUIRED 1 2 class periods GRADES SUBJECTS Physics Techology/Egieerig Mathematics BACKGROUND The blades of a wid turbie have the most importat job of ay wid turbie compoet ; they must capture the wid ad covert it ito usable mechaical eergy. Over time, egieers have experimeted with may differet shapes, desigs, materials, ad umbers of blades to fid which work best. This lesso explores how egieers determie the optimal blade desig. OBJECTIVES At the ed of the lesso, studets will: uderstad how wid eergy is coverted to electricity kow the process of scietific iquiry to test blade desig variables be able to collect, evaluate, ad preset data to determie which blade desig is best uderstad the egieerig desig process METHOD Studets will use wid turbie kits to test differet variables i blade desig ad measure the power output of each. Each group of studets will isolate oe variable of wid turbie blade desig, the collect ad preset data for that variable. If time allows, studets ca use their collected data to desig a optimal set of wid turbie blades usig the ext lesso, How Ca I Desig a Better Blade? MATERIALS You will eed oe set of the followig materials for each group: 1 model turbie o which blades ca quickly be iterchaged 1 multimeter or voltage/curret data logger 1 box fa Milk cartos, PVC pipe, or paper towel rolls (optioal) Ruler Pictures of wid turbie blades (see the Blade Desig PowerPoit show i Additioal Resources) Sample blades of varyig sizes, shapes, ad materials Balsa wood, corrugated plastic, cardstock, paper plates, etc. ¼" dowels Duct tape ad/or hot glue Scissors Protractor for measurig blade pitch Safety glasses Poster-size graph paper (optioal) Studet Worksheets* *icluded with this activity 187

4 WHICH BLADES ARE BEST? REDUCE DRAG More Drag Less Drag GETTING READY Studets should already have a basic uderstadig of wid eergy, icludig the followig: what a wid turbie is the fudametal parts of a wid turbie how wid turbies trasform eergy from the wid basic variables that impact turbie performace Most of this backgroud was covered i the lesso How Does a Widmill Work? The additioal resources listed at the ed of this lesso also provide helpful iformatio. The Blade Desig PowerPoit foud i the Additioal Resources sectio will also be helpful for this lesso. This slideshow features descriptios of differet blade desigs ad close-up pictures of wid turbie blades. Set up a safe testig area. Clear this area of debris ad materials. Make sure the ceter of the fa is aliged with the ceter of the wid turbie. If you are workig with multiple turbies, set them up so studets will ot be stadig i the plae of rotatio of a earby turbie. Prepare three or four simple blade sets as samples for studets to begi to see several variables ad figure out how to build blades. Make sure the sample blade sets display differet blade variables, such as legth, material, ad umber of blades. Make copies of worksheets. ACTIVITY Step 1: Begiig questios for studets What do you thik makes oe turbie work better tha aother? What variables affect the amout of power a turbie ca geerate? Do some variables matter more tha others? (For example, is turbie height more importat tha the umber of blades?) What do moder wid turbie blades look like? Is this similar to those o older widmills? Why? How may blades do most wid turbies have? What do you thik would happe with more or fewer blades? Step 2: Braistorm blade variables Provide studets with photos of differet turbie desigs, usig the Blade Desig PowerPoit or other photos foud i the Additioal Resources. Ask studets to braistorm some of the variables that affect how much eergy the blades ca capture while they are lookig at the photos. WidWiseEducatio.org Variables may iclude: blade legth umber of blades weight/distributio of weight o blade blade pitch/agle blade shape blade material blade twist 188 Lesso 10

5 WHICH BLADES ARE BEST? Step 3: Determiig variables Orgaize studets ito small groups. Four studets per group is optimal. Give each studet a worksheet. Have each group select oe variable to test. Legth, umber, pitch/agle, ad shape are easy variables to test, but studets ca come up with additioal variables as well. Before costructig blades, groups should determie what eeds to be held costat i order to effectively test their variables. If you are coductig this exercise as a demostratio, ask studets which variable will perform better ad why before testig it. Studets will complete their worksheets while the teacher tests each variable. Studets ca take turs attachig blades or readig the multimeter. Step 4: Buildig blades Depedig o the variable beig tested, some groups will have to build multiple sets of blades, while other groups will oly build oe set. For example, the group testig blade material will have to build oe set of idetical blades with each material beig tested. The group testig pitch/agle, however, will oly build oe set of blades ad the test the agle of these blades o the turbie. Groups should collect their blade materials, the work together to costruct blades. Step 5: Testig blades The group will attach each set of blades to the turbie ad test it at both high ad low wid speeds. The group ca chage wid speed by movig the turbie away from the fa or turig the fa lower. Wid comig from a fa is very turbulet ad does ot accurately represet the wid a turbie would experiece outside. To clea up this turbulet wid, studets ca make a wid tuel by buildig a hoeycomb i frot of the fa usig milk cartos, PVC pipe, or paper towel rolls. This will slow the wid comig off the fa, but it will also straighte it out. BLADE PITCH Blade pitch is the agle of the blades with respect to the plae of rotatio. The pitch of the blades dramatically affects the amout of drag experieced by the blades. Efficiet blades will provide maximum torque with miimum drag. Measure pitch with a protractor. 0º 45º 90º Be sure studets uderstad what blade pitch (agle) is ad how they will measure it or keep it costat. This cocept was itroduced i How Does a Widmill Work? Make sure that studets keep pitch costat while testig other variables or the results ca be problematic. Studets will measure the voltage with a multimeter ad record their data o the worksheet. If time permits, ask studets to do three replicatios of each variable ad average their results. Step 6: Aalysis Oce studets have collected their data, tell them to aswer the questios o the worksheet ad make a graph of their data to preset to the class. If poster-size graph paper is available for studets, ask them to replicate the graph o this paper for their presetatios. WidWiseEducatio.org Lesso

6 WHICH BLADES ARE BEST? CAUTION! Do ot stad i the plae of rotatio of the rotor! You could be hit if your blade flies off durig testig. The spiig rotor blades ad metal rod ca be dagerous. Make sure studets work with cautio. Be careful whe workig with the metal rod. Do ot swig or play with the rod! The eds ca be protected with tape, foam, cork, etc. Wear safety glasses whe testig widmills. Safety glasses must be wor ay time blades are spiig. Plae of rotatio: do t stad here! Stad behid or i frot of the plae of rotatio - ad wear safety glasses! Step 7: Presetatio Each group will have five miutes to preset its data to the class. Studets should discuss their variables, how they desiged the blades, ad the results. Ask all the studets to record the results from each group o their worksheets so they have all of the class results. Step 8: Wrap up Wrap up the lesso with some of the followig questios: What variable has the greatest impact o power output? What type of blades worked best at low speeds? High speeds? What umber of blades worked best? What shapes worked best? What legth worked best? What problems did you ecouter? Did loger blades bed backward i the wid? Was this a problem? What happeed whe the diameter of the turbie rotor was bigger tha the diameter of the fa? Ask studets to aalyze the class data ad describe a optimal blade desig. If time permits, this ca be used as a startig poit for the extesio lesso: How Ca I Desig a Better Blade? EXTENSION The followig extesio may be made for grades 9 12: Ask studets to also collect amperage data ad calculate power. Discuss voltage, amperage, ad power ad how they relate to oe aother. Ask studets to determie the efficiecy of their turbies. The efficiecy of a turbie is a compariso betwee the theoretical power available i the wid ad the actual power output of the turbie. To calculate the theoretical power i the wid, studets ca use this equatio: P = ½ ρ (π r 2 )V 3 P = total power available i the wid ρ = air desity (1.23 kg/m 3 at sea level) π = pi (3.14) r = rotor radius (legth of oe blade) V = velocity of the wid WidWiseEducatio.org Turbie efficiecy is equal to the total power output of the turbie divided by the theoretical power available. Do ot be surprised if your efficiecy is uder 5 percet. The maximum theoretical efficiecy of a wid geerator is 59 percet. Research Betz Limit to lear more about this. 190 Lesso 10

7 WHICH BLADES ARE BEST? VOCABULARY amperage A measure of the rate of flow of electrical charges. 1 ampere = 1 volt = 1 watt or I amp = V = P 1 ohm 1 volt R V blade pitch Agle of the blades with respect to the plae of rotatio. (Blades perpedicular to the ocomig wid would be 0 degrees. Blades parallel to the wid would be 90 degrees). drag I a wid turbie, also called wid resistace. The frictio of the blades agaist air molecules as they rotate. Drag works agaist the rotatio of the blades, causig them to slow dow. lift A force ecoutered by the blades that is perpedicular to the ocomig flow of air. Lift is a force workig to speed up the rotatio of the blades. multimeter A electroic istrumet that ca measure voltage, curret, ad resistace. power The rate at which eergy chages form from oe form to aother, or the rate at which work is doe voltage The electrical pressure or potetial differece that drives the electric curret. 1 volt = 1 amps 1 ohm = 1 watts / 1 amps wattage the metric uit of power. I electricity, oe watt of power is equal to oe ampere of electric curret beig forced to move by oe volt of potetial differece. Oe watt is also equivalet to oe joule of eergy per secod. 1 watt = 1 volt 1 amp. USE A MULTIMETER WITH YOUR WIND TURBINE Studets eed to kow how to record voltage ad amperage with a simple multimeter. Make sure you have doe this yourself ad ca explai it to the studets. It is importat to esure that the uits are correct. If you multiply volts by milliamps, you will get a cofusigly large ad icorrect umber for power. It is okay to just record voltage, which ca make thigs easier. Small DC motors do ot produce much power whe spu slowly. A wid turbie without gears will ot get more tha 2 volts. O a wid turbie with gears, power output ca be icreased (2 8 volts) usig gears to spi the shaft of the geerator faster tha the hub. Go to for a video o usig a multimeter. Lesso WidWiseEducatio.org

8 WHICH BLADES ARE BEST? RELATED ACTIVITIES Lesso 8: How Does a Widmill Work? Lesso 11: How Ca I Desig Better Blades? Advaced Blades Appedix ADDITIONAL RESOURCES DANISH WIND ENERGY ASSOCIATION Guided Tour: How Does It Work? KIDWIND, CLASSROOM WIND TURBINES KidWid has compiled a list of ideas for buildig your ow wid turbie. This site also icludes complete kits, istructios o how to build model turbies, ad more ideas for classroom activities. KIDWIND, WIND TURBINE VARIABLES This site explais the differet wid turbie variables. KIDWIND WEB COMPETITION Show-off your small wid turbie buildig skills. WIND TURBINE BLADE DESIGN PowerPoit slide show WIND WITH MILLER This is a good itroductio to wid eergy ad wid turbies. Great for grades 6 8. More advaced explaatios of wid turbie sciece, better for grades NATIONAL RENEWABLE ENERGY LABORATORY Search for wid turbies ad blades; you will also fid a wide rage of wid eergy images. WidWiseEducatio.org 192 Lesso 10

9 Which Blades Are Best? Studet sheets ENERGY TRANSFERS AND CONVERSIONS IN A TURBINE Blades up to 60 m log Wid at least 8 m/s Blades rotate RPM m tall 1. Blades attached to hub (rotor spis i the wid) 2. Spis drive shaft (trasfers force to gearbox) 3. Gearbox (icreases shaft speed) 4. High speed shaft (trasfers force to geerator) 5. Geerator (coverts spiig shaft to electricity) 6. Wires to grid (provides electricity) 6 Lesso 10 WidWiseEducatio.org 193

10 Which Blades Are Best? Studet sheets Name Date Class Variable What variable will you test for your experimet? Costats What variables do you have to keep the same (costat) as you perform this experimet? Experimetal desig Describe how you will perform this experimet. 1. What materials will you use? 2. How may times will you test your variable? 3. How log will you ru the test? 4. How will you chage your variable? 5. What will you use to measure your output? Hypothesis 1. What do you thik will happe? 2. Why do you thik this will happe? 194 WidWiseEducatio.org Lesso 10

11 Which Blades Are Best? Studet sheets Data tally sheet : grades 6 8 VARIABLE (e.g., legth, i cm) LOW SPEED VOLTAGE (mv or V) HIGH SPEED VOLTAGE (mv or V) Graph your data Voltage output Variable tested (legth, umber, etc.) Lesso 10 WidWiseEducatio.org 195

12 Which Blades Are Best? Studet sheets Data tally sheet: grades 9 12 LOW SPEED VARIABLE VOLTAGE (e.g., legth, i cm) (mv or V) AMPERAGE (ma or A) (V A) = POWER (mw or W) HIGH SPEED VARIABLE (e.g., legth, i cm) VOLTAGE (mv or V) AMPERAGE (ma or A) (V A) = POWER (mw or W) Graph your data Voltage output Variable tested (legth, umber, etc.) 196 WidWiseEducatio.org Lesso 10

13 Which Blades Are Best? Studet sheets Name Date Class What happeed? 1. How did the voltage chage as a result of maipulatig the variable? 2. What was the optimal settig for the variable that you tested? 3. Do you thik that the variable that you tested has a large or small effect o how much power the turbie ca make? 4. What problems did you ecouter as you performed your experimets? How could you fix these problems? Lesso 10 WidWiseEducatio.org 197

14 Which Blades Are Best? Studet sheets Class results Record the results from the class experimets i the table below. Power = Voltage (V) Curret (A) Make sure you are recordig volts ad amps (ot milliamps). 1 A=1,000 ma VARIABLE VOLTAGE (V) AMPERAGE POWER OUTPUT (e.g. legth cm) (extesio) (ma or A) (optioal) (mw or W) 15 cm ma 0.17 W 1. If you were a lead desig egieer, what would you recommed your compay do to their turbie blades based o the class results? Why? 198 WidWiseEducatio.org Lesso 10

15 Which Blades Are Best? Aswer sheets Variable What variable will you test for your experimet? Aswers will vary. Example variables: Blade pitch, blade shape/size, material of blades, umber of blades, etc. Costats What variables do you have to keep the same (costat) as you perform this experimet? Aswers will vary. Example variables: Blade pitch, blade shape/size, material of blades, umber of blades, etc. Experimetal desig Describe how you will perform this experimet. 1. What materials will you use? Aswers will vary. Balsa, corrugated plastic, paper plates, cardboard, etc. 2. How may times will you test your variable? Variables should be tested at least twice. 3. How log will you ru the test? Aswers will vary. Trials should last at least 20 secods. 4. How will you chage your variable? Aswers will vary. 5. What will you use to measure your output? Output should be recorded usig a multimeter or other quatitative measuremet. Hypothesis 1. What do you thik will happe? Studets should hypothesize about how chagig their chose variable will affect the power output of the wid turbie. 2. Why do you thik this will happe? Studets should explai why they thik chagig the variable will affect power i this way. What happeed? 1. How did the voltage chage as a result of maipulatig your variable? Chagig the variable should cause the voltage to icrease or decrease. 2. What was the optimal settig for the variable that you tested? Which trial yielded the most voltage? For example, if the test variable is blade pitch, studets may aswer Blades pitched at 20 degrees produced the most voltage. 3. Do you thik that your variable has a large or small effect o how much power the turbie ca make? Aswers will vary. Lesso 10 WidWiseEducatio.org 199

16 Which Blades Are Best? Aswer sheets 4. What problems did you ecouter as you performed your experimets? How could you fix these problems? Aswers will vary. Oe commo problem is that it is hard to keep all other variables costat while testig oe specific variable. Class results Record the results from the class experimets i the table below. Power = Voltage (V) Curret (A) 1. If you were a lead desig egieer, what would you recommed your compay do to their turbie blades based o the class results? Why? Studets should describe the optimal blade desig based o class results. This aswer should discuss at least three variables e.g., legth of blades, umber of blades, blade pitch, blade material, etc. 200 WidWiseEducatio.org Lesso 10

Lesson 17 Pearson s Correlation Coefficient

Lesson 17 Pearson s Correlation Coefficient Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

Mathematical goals. Starting points. Materials required. Time needed

Mathematical goals. Starting points. Materials required. Time needed Level A1 of challege: C A1 Mathematical goals Startig poits Materials required Time eeded Iterpretig algebraic expressios To help learers to: traslate betwee words, symbols, tables, ad area represetatios

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

More information

Measuring Magneto Energy Output and Inductance Revision 1

Measuring Magneto Energy Output and Inductance Revision 1 Measurig Mageto Eergy Output ad Iductace evisio Itroductio A mageto is fudametally a iductor that is mechaically charged with a iitial curret value. That iitial curret is produced by movemet of the rotor

More information

LIFE CYCLES UNIT OVERVIEW THE BIG IDEA. Other topics SPARK. Materials. Activity

LIFE CYCLES UNIT OVERVIEW THE BIG IDEA. Other topics SPARK. Materials. Activity LIFE CYCLES UNIT OVERVIEW All livig thigs go through chages as they grow ad develop. Although idividual orgaisms die, ew oes replace them, which esures the survival of the species. Durig its life cycle,

More information

G r a d e. 2 M a t h e M a t i c s. statistics and Probability

G r a d e. 2 M a t h e M a t i c s. statistics and Probability G r a d e 2 M a t h e M a t i c s statistics ad Probability Grade 2: Statistics (Data Aalysis) (2.SP.1, 2.SP.2) edurig uderstadigs: data ca be collected ad orgaized i a variety of ways. data ca be used

More information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

More information

HCL Dynamic Spiking Protocol

HCL Dynamic Spiking Protocol ELI LILLY AND COMPANY TIPPECANOE LABORATORIES LAFAYETTE, IN Revisio 2.0 TABLE OF CONTENTS REVISION HISTORY... 2. REVISION.0... 2.2 REVISION 2.0... 2 2 OVERVIEW... 3 3 DEFINITIONS... 5 4 EQUIPMENT... 7

More information

Quadrat Sampling in Population Ecology

Quadrat Sampling in Population Ecology Quadrat Samplig i Populatio Ecology Backgroud Estimatig the abudace of orgaisms. Ecology is ofte referred to as the "study of distributio ad abudace". This beig true, we would ofte like to kow how may

More information

WindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12

WindWise Education. 2 nd. T ransforming the Energy of Wind into Powerful Minds. editi. A Curriculum for Grades 6 12 WindWise Education T ransforming the Energy of Wind into Powerful Minds A Curriculum for Grades 6 12 Notice Except for educational use by an individual teacher in a classroom setting this work may not

More information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread and Boxplots Discrete Math, Section 9.4 Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

More information

Baan Service Master Data Management

Baan Service Master Data Management Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :

More information

Chapter 7: Confidence Interval and Sample Size

Chapter 7: Confidence Interval and Sample Size Chapter 7: Cofidece Iterval ad Sample Size Learig Objectives Upo successful completio of Chapter 7, you will be able to: Fid the cofidece iterval for the mea, proportio, ad variace. Determie the miimum

More information

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means)

CHAPTER 7: Central Limit Theorem: CLT for Averages (Means) CHAPTER 7: Cetral Limit Theorem: CLT for Averages (Meas) X = the umber obtaied whe rollig oe six sided die oce. If we roll a six sided die oce, the mea of the probability distributio is X P(X = x) Simulatio:

More information

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number.

GCSE STATISTICS. 4) How to calculate the range: The difference between the biggest number and the smallest number. GCSE STATISTICS You should kow: 1) How to draw a frequecy diagram: e.g. NUMBER TALLY FREQUENCY 1 3 5 ) How to draw a bar chart, a pictogram, ad a pie chart. 3) How to use averages: a) Mea - add up all

More information

(VCP-310) 1-800-418-6789

(VCP-310) 1-800-418-6789 Maual VMware Lesso 1: Uderstadig the VMware Product Lie I this lesso, you will first lear what virtualizatio is. Next, you ll explore the products offered by VMware that provide virtualizatio services.

More information

Professional Networking

Professional Networking Professioal Networkig 1. Lear from people who ve bee where you are. Oe of your best resources for etworkig is alumi from your school. They ve take the classes you have take, they have bee o the job market

More information

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the

More information

Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.

Here are a couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. This documet was writte ad copyrighted by Paul Dawkis. Use of this documet ad its olie versio is govered by the Terms ad Coditios of Use located at http://tutorial.math.lamar.edu/terms.asp. The olie versio

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

Determining the sample size

Determining the sample size Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors

More information

Basic Measurement Issues. Sampling Theory and Analog-to-Digital Conversion

Basic Measurement Issues. Sampling Theory and Analog-to-Digital Conversion Theory ad Aalog-to-Digital Coversio Itroductio/Defiitios Aalog-to-digital coversio Rate Frequecy Aalysis Basic Measuremet Issues Reliability the extet to which a measuremet procedure yields the same results

More information

CS100: Introduction to Computer Science

CS100: Introduction to Computer Science I-class Exercise: CS100: Itroductio to Computer Sciece What is a flip-flop? What are the properties of flip-flops? Draw a simple flip-flop circuit? Lecture 3: Data Storage -- Mass storage & represetig

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized? 5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

5: Introduction to Estimation

5: Introduction to Estimation 5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

More information

Hypergeometric Distributions

Hypergeometric Distributions 7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

Ideate, Inc. Training Solutions to Give you the Leading Edge

Ideate, Inc. Training Solutions to Give you the Leading Edge Ideate, Ic. Traiig News 2014v1 Ideate, Ic. Traiig Solutios to Give you the Leadig Edge New Packages For All Your Traiig Needs! Bill Johso Seior MEP - Applicatio Specialist Revit MEP Fudametals Ad More!

More information

CS100: Introduction to Computer Science

CS100: Introduction to Computer Science Review: History of Computers CS100: Itroductio to Computer Sciece Maiframes Miicomputers Lecture 2: Data Storage -- Bits, their storage ad mai memory Persoal Computers & Workstatios Review: The Role of

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

A Guide to the Pricing Conventions of SFE Interest Rate Products

A Guide to the Pricing Conventions of SFE Interest Rate Products A Guide to the Pricig Covetios of SFE Iterest Rate Products SFE 30 Day Iterbak Cash Rate Futures Physical 90 Day Bak Bills SFE 90 Day Bak Bill Futures SFE 90 Day Bak Bill Futures Tick Value Calculatios

More information

I. Why is there a time value to money (TVM)?

I. Why is there a time value to money (TVM)? Itroductio to the Time Value of Moey Lecture Outlie I. Why is there the cocept of time value? II. Sigle cash flows over multiple periods III. Groups of cash flows IV. Warigs o doig time value calculatios

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

How to set up your GMC Online account

How to set up your GMC Online account How to set up your GMC Olie accout Mai title Itroductio GMC Olie is a secure part of our website that allows you to maage your registratio with us. Over 100,000 doctors already use GMC Olie. We wat every

More information

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature. Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

More information

Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.

Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern. 5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers

More information

Agenda. Outsourcing and Globalization in Software Development. Outsourcing. Outsourcing here to stay. Outsourcing Alternatives

Agenda. Outsourcing and Globalization in Software Development. Outsourcing. Outsourcing here to stay. Outsourcing Alternatives Outsourcig ad Globalizatio i Software Developmet Jacques Crocker UW CSE Alumi 2003 jc@cs.washigto.edu Ageda Itroductio The Outsourcig Pheomeo Leadig Offshore Projects Maagig Customers Offshore Developmet

More information

Engineering Data Management

Engineering Data Management BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P EXEMPLAR 04 MARKS: 50 TIME: 3 hours This questio paper cosists of 8 pages ad iformatio sheet. Please tur over Mathematics/P DBE/04 NSC Grade Eemplar INSTRUCTIONS

More information

Building Blocks Problem Related to Harmonic Series

Building Blocks Problem Related to Harmonic Series TMME, vol3, o, p.76 Buildig Blocks Problem Related to Harmoic Series Yutaka Nishiyama Osaka Uiversity of Ecoomics, Japa Abstract: I this discussio I give a eplaatio of the divergece ad covergece of ifiite

More information

Project Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments

Project Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments Project Deliverables CS 361, Lecture 28 Jared Saia Uiversity of New Mexico Each Group should tur i oe group project cosistig of: About 6-12 pages of text (ca be loger with appedix) 6-12 figures (please

More information

7.1 Finding Rational Solutions of Polynomial Equations

7.1 Finding Rational Solutions of Polynomial Equations 4 Locker LESSON 7. Fidig Ratioal Solutios of Polyomial Equatios Name Class Date 7. Fidig Ratioal Solutios of Polyomial Equatios Essetial Questio: How do you fid the ratioal roots of a polyomial equatio?

More information

AP Calculus BC 2003 Scoring Guidelines Form B

AP Calculus BC 2003 Scoring Guidelines Form B AP Calculus BC Scorig Guidelies Form B The materials icluded i these files are iteded for use by AP teachers for course ad exam preparatio; permissio for ay other use must be sought from the Advaced Placemet

More information

Basic Elements of Arithmetic Sequences and Series

Basic Elements of Arithmetic Sequences and Series MA40S PRE-CALCULUS UNIT G GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elemets of Arithmetic Sequeces ad Series Objective: To establish basic elemets of arithmetic

More information

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here).

Example 2 Find the square root of 0. The only square root of 0 is 0 (since 0 is not positive or negative, so those choices don t exist here). BEGINNING ALGEBRA Roots ad Radicals (revised summer, 00 Olso) Packet to Supplemet the Curret Textbook - Part Review of Square Roots & Irratioals (This portio ca be ay time before Part ad should mostly

More information

National Institute on Aging. What Is A Nursing Home?

National Institute on Aging. What Is A Nursing Home? Natioal Istitute o Agig AgePage Nursig Homes: Makig The Right Choice Lucille has lived i her home for 33 years. Eve after her husbad died 3 years ago, she was able to maage o her ow. Recetly, she broke

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Using Four Types Of Notches For Comparison Between Chezy s Constant(C) And Manning s Constant (N)

Using Four Types Of Notches For Comparison Between Chezy s Constant(C) And Manning s Constant (N) INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH OLUME, ISSUE, OCTOBER ISSN - Usig Four Types Of Notches For Compariso Betwee Chezy s Costat(C) Ad Maig s Costat (N) Joyce Edwi Bategeleza, Deepak

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology

More information

Conversion Instructions:

Conversion Instructions: Coversio Istructios: QMS magicolor 2 DeskLaser to QMS magicolor 2 CX 1800502-001A Trademarks QMS, the QMS logo, ad magicolor are registered trademarks of QMS, Ic., registered i the Uited States Patet ad

More information

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chi-square (χ ) distributio.

More information

COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S 2 CONTROL CHART FOR THE CHANGES IN A PROCESS

COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S 2 CONTROL CHART FOR THE CHANGES IN A PROCESS COMPARISON OF THE EFFICIENCY OF S-CONTROL CHART AND EWMA-S CONTROL CHART FOR THE CHANGES IN A PROCESS Supraee Lisawadi Departmet of Mathematics ad Statistics, Faculty of Sciece ad Techoology, Thammasat

More information

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction

THE ARITHMETIC OF INTEGERS. - multiplication, exponentiation, division, addition, and subtraction THE ARITHMETIC OF INTEGERS - multiplicatio, expoetiatio, divisio, additio, ad subtractio What to do ad what ot to do. THE INTEGERS Recall that a iteger is oe of the whole umbers, which may be either positive,

More information

Automatic Tuning for FOREX Trading System Using Fuzzy Time Series

Automatic Tuning for FOREX Trading System Using Fuzzy Time Series utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which

More information

Flood Emergency Response Plan

Flood Emergency Response Plan Flood Emergecy Respose Pla This reprit is made available for iformatioal purposes oly i support of the isurace relatioship betwee FM Global ad its cliets. This iformatio does ot chage or supplemet policy

More information

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the.

Confidence Intervals. CI for a population mean (σ is known and n > 30 or the variable is normally distributed in the. Cofidece Itervals A cofidece iterval is a iterval whose purpose is to estimate a parameter (a umber that could, i theory, be calculated from the populatio, if measuremets were available for the whole populatio).

More information

AP Calculus AB 2006 Scoring Guidelines Form B

AP Calculus AB 2006 Scoring Guidelines Form B AP Calculus AB 6 Scorig Guidelies Form B The College Board: Coectig Studets to College Success The College Board is a ot-for-profit membership associatio whose missio is to coect studets to college success

More information

For customers Key features of the Guaranteed Pension Annuity

For customers Key features of the Guaranteed Pension Annuity For customers Key features of the Guarateed Pesio Auity The Fiacial Coduct Authority is a fiacial services regulator. It requires us, Aego, to give you this importat iformatio to help you to decide whether

More information

2-3 The Remainder and Factor Theorems

2-3 The Remainder and Factor Theorems - The Remaider ad Factor Theorems Factor each polyomial completely usig the give factor ad log divisio 1 x + x x 60; x + So, x + x x 60 = (x + )(x x 15) Factorig the quadratic expressio yields x + x x

More information

CREATIVE MARKETING PROJECT 2016

CREATIVE MARKETING PROJECT 2016 CREATIVE MARKETING PROJECT 2016 The Creative Marketig Project is a chapter project that develops i chapter members a aalytical ad creative approach to the marketig process, actively egages chapter members

More information

How to use what you OWN to reduce what you OWE

How to use what you OWN to reduce what you OWE How to use what you OWN to reduce what you OWE Maulife Oe A Overview Most Caadias maage their fiaces by doig two thigs: 1. Depositig their icome ad other short-term assets ito chequig ad savigs accouts.

More information

Output Analysis (2, Chapters 10 &11 Law)

Output Analysis (2, Chapters 10 &11 Law) B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

More information

Case Study. Normal and t Distributions. Density Plot. Normal Distributions

Case Study. Normal and t Distributions. Density Plot. Normal Distributions Case Study Normal ad t Distributios Bret Halo ad Bret Larget Departmet of Statistics Uiversity of Wiscosi Madiso October 11 13, 2011 Case Study Body temperature varies withi idividuals over time (it ca

More information

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean

Definition. A variable X that takes on values X 1, X 2, X 3,...X k with respective frequencies f 1, f 2, f 3,...f k has mean 1 Social Studies 201 October 13, 2004 Note: The examples i these otes may be differet tha used i class. However, the examples are similar ad the methods used are idetical to what was preseted i class.

More information

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model

Trading the randomness - Designing an optimal trading strategy under a drifted random walk price model Tradig the radomess - Desigig a optimal tradig strategy uder a drifted radom walk price model Yuao Wu Math 20 Project Paper Professor Zachary Hamaker Abstract: I this paper the author iteds to explore

More information

Elementary Theory of Russian Roulette

Elementary Theory of Russian Roulette Elemetary Theory of Russia Roulette -iterestig patters of fractios- Satoshi Hashiba Daisuke Miematsu Ryohei Miyadera Itroductio. Today we are goig to study mathematical theory of Russia roulette. If some

More information

How to read A Mutual Fund shareholder report

How to read A Mutual Fund shareholder report Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.

More information

15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011

15.075 Exam 3. Instructor: Cynthia Rudin TA: Dimitrios Bisias. November 22, 2011 15.075 Exam 3 Istructor: Cythia Rudi TA: Dimitrios Bisias November 22, 2011 Gradig is based o demostratio of coceptual uderstadig, so you eed to show all of your work. Problem 1 A compay makes high-defiitio

More information

Setting Up a Contract Action Network

Setting Up a Contract Action Network CONTRACT ACTION NETWORK Settig Up a Cotract Actio Network This is a guide for local uio reps who wat to set up a iteral actio etwork i their worksites. This etwork cosists of: The local uio represetative,

More information

PUBLIC RELATIONS PROJECT 2016

PUBLIC RELATIONS PROJECT 2016 PUBLIC RELATIONS PROJECT 2016 The purpose of the Public Relatios Project is to provide a opportuity for the chapter members to demostrate the kowledge ad skills eeded i plaig, orgaizig, implemetig ad evaluatig

More information

ODBC. Getting Started With Sage Timberline Office ODBC

ODBC. Getting Started With Sage Timberline Office ODBC ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

auction a guide to selling at Residential

auction a guide to selling at Residential Residetial a guide to sellig at auctio Allsop is the market leader for residetial ad commercial auctios i the UK Aually sells up to 700 millio of property at auctio Holds at least seve residetial ad six

More information

Desktop Management. Desktop Management Tools

Desktop Management. Desktop Management Tools Desktop Maagemet 9 Desktop Maagemet Tools Mac OS X icludes three desktop maagemet tools that you might fid helpful to work more efficietly ad productively: u Stacks puts expadable folders i the Dock. Clickig

More information

MEETING OF THE GRADUATE ASSEMBLY THE UNIVERSITY OF TEXAS AT ARLINGTON. February 15, 2001

MEETING OF THE GRADUATE ASSEMBLY THE UNIVERSITY OF TEXAS AT ARLINGTON. February 15, 2001 DRAFT GA 02-3-1 MEETING OF THE GRADUATE ASSEMBLY THE UNIVERSITY OF TEXAS AT ARLINGTON February 15, 2001 The Graduate Assembly meetig of February 15, 2001 was called to order by Chair K. Behbehai at 2:30

More information

1 Correlation and Regression Analysis

1 Correlation and Regression Analysis 1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

NATIONAL SENIOR CERTIFICATE GRADE 11

NATIONAL SENIOR CERTIFICATE GRADE 11 NATIONAL SENIOR CERTIFICATE GRADE MATHEMATICS P NOVEMBER 007 MARKS: 50 TIME: 3 hours This questio paper cosists of 9 pages, diagram sheet ad a -page formula sheet. Please tur over Mathematics/P DoE/November

More information

Now here is the important step

Now here is the important step LINEST i Excel The Excel spreadsheet fuctio "liest" is a complete liear least squares curve fittig routie that produces ucertaity estimates for the fit values. There are two ways to access the "liest"

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond

Bond Valuation I. What is a bond? Cash Flows of A Typical Bond. Bond Valuation. Coupon Rate and Current Yield. Cash Flows of A Typical Bond What is a bod? Bod Valuatio I Bod is a I.O.U. Bod is a borrowig agreemet Bod issuers borrow moey from bod holders Bod is a fixed-icome security that typically pays periodic coupo paymets, ad a pricipal

More information

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows: Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network

More information

The Canadian Council of Professional Engineers

The Canadian Council of Professional Engineers The Caadia Coucil of Professioal Egieers Providig leadership which advaces the quality of life through the creative, resposible ad progressive applicatio of egieerig priciples i a global cotext Egieerig

More information

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals

Overview. Learning Objectives. Point Estimate. Estimation. Estimating the Value of a Parameter Using Confidence Intervals Overview Estimatig the Value of a Parameter Usig Cofidece Itervals We apply the results about the sample mea the problem of estimatio Estimatio is the process of usig sample data estimate the value of

More information

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10

FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 FOUNDATIONS OF MATHEMATICS AND PRE-CALCULUS GRADE 10 [C] Commuicatio Measuremet A1. Solve problems that ivolve liear measuremet, usig: SI ad imperial uits of measure estimatio strategies measuremet strategies.

More information

Confidence Intervals for One Mean

Confidence Intervals for One Mean Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

More information

One Goal. 18-Months. Unlimited Opportunities.

One Goal. 18-Months. Unlimited Opportunities. 18 fast-track 18-Moth BACHELOR S DEGREE completio PROGRAMS Oe Goal. 18-Moths. Ulimited Opportuities. www.ortheaster.edu/cps Fast-Track Your Bachelor s Degree ad Career Goals Complete your bachelor s degree

More information

Get advice now. Are you worried about your mortgage? New edition

Get advice now. Are you worried about your mortgage? New edition New editio Jauary 2009 Are you worried about your mortgage? Get advice ow If you are strugglig to pay your mortgage, or you thik it will be difficult to pay more whe your fixed-rate deal eds, act ow to

More information

Simple Annuities Present Value.

Simple Annuities Present Value. Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

More information

Solving equations. Pre-test. Warm-up

Solving equations. Pre-test. Warm-up Solvig equatios 8 Pre-test Warm-up We ca thik of a algebraic equatio as beig like a set of scales. The two sides of the equatio are equal, so the scales are balaced. If we add somethig to oe side of the

More information

Lesson 15 ANOVA (analysis of variance)

Lesson 15 ANOVA (analysis of variance) Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi

More information

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

More information

Student #41 Environmental Science 1-7-2015

Student #41 Environmental Science 1-7-2015 Student #41 Environmental Science 1-7-2015 Introduction: Wind energy is the energy extracted from wind using wind turbines to produce electrical power, windmills for mechanical power, wind pumps for water

More information

Pre-Suit Collection Strategies

Pre-Suit Collection Strategies Pre-Suit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process

More information

Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships

Biology 171L Environment and Ecology Lab Lab 2: Descriptive Statistics, Presenting Data and Graphing Relationships Biology 171L Eviromet ad Ecology Lab Lab : Descriptive Statistics, Presetig Data ad Graphig Relatioships Itroductio Log lists of data are ofte ot very useful for idetifyig geeral treds i the data or the

More information

The Forgotten Middle. research readiness results. Executive Summary

The Forgotten Middle. research readiness results. Executive Summary The Forgotte Middle Esurig that All Studets Are o Target for College ad Career Readiess before High School Executive Summary Today, college readiess also meas career readiess. While ot every high school

More information