Adding Percentage Error
Contents |
dividing Is one result consistent with another? What if there are several measurements of the same quantity? How can one estimate the uncertainty of a slope on a graph? Uncertainty in a single measurement Bob weighs himself on his bathroom scale. The smallest divisions on the scale are 1-pound marks, so the least count of the instrument is percentage error calculator 1 pound. Bob reads his weight as closest to the 142-pound mark. He knows his weight must percentage error chemistry be larger than 141.5 pounds (or else it would be closer to the 141-pound mark), but smaller than 142.5 pounds (or else it would be percentage error calculus closer to the 143-pound mark). So Bob's weight must be weight = 142 +/- 0.5 pounds In general, the uncertainty in a single measurement from a single instrument is half the least count of the instrument. Fractional and percentage uncertainty What is negative percentage error the fractional uncertainty in Bob's weight? uncertainty in weight fractional uncertainty = ------------------------ value for weight 0.5 pounds = ------------- = 0.0035 142 pounds What is the uncertainty in Bob's weight, expressed as a percentage of his weight? uncertainty in weight percentage uncertainty = ----------------------- * 100% value for weight 0.5 pounds = ------------ * 100% = 0.35% 142 pounds Combining uncertainties in several quantities: adding or subtracting When one adds or subtracts several measurements together, one simply adds together the uncertainties to find the
Percentage Error Theoretical Experimental
uncertainty in the sum. Dick and Jane are acrobats. Dick is 186 +/- 2 cm tall, and Jane is 147 +/- 3 cm tall. If Jane stands on top of Dick's head, how far is her head above the ground? combined height = 186 cm + 147 cm = 333 cm uncertainty in combined height = 2 cm + 3 cm = 5 cm combined height = 333 cm +/- 5 cm Now, if all the quantities have roughly the same magnitude and uncertainty -- as in the example above -- the result makes perfect sense. But if one tries to add together very different quantities, one ends up with a funny-looking uncertainty. For example, suppose that Dick balances on his head a flea (ick!) instead of Jane. Using a pair of calipers, Dick measures the flea to have a height of 0.020 cm +/- 0.003 cm. If we follow the rules, we find combined height = 186 cm + 0.020 cm = 186.020 cm uncertainty in combined height = 2 cm + 0.003 cm = 2.003 cm ??? combined height = 186.020 cm +/- 2.003 cm ??? But wait a minute! This doesn't make any sense! If we can't tell exactly where the top of Dick's head is to within a couple of cm, what difference does it make if the flea is 0.020 cm or 0.021 cm tall? In technical terms, the number of significant figures required to express the sum of the two heights is far more than either measuremen
Example: I estimated 260 people, but 325 came. 260 − 325 = −65, ignore the "−" sign, so my error is 65 "Percentage Error": show the error as
Percentage Error Wiki
a percent of the exact value ... so divide by the exact percentage error definition value and make it a percentage: 65/325 = 0.2 = 20% Percentage Error is all about comparing a guess percentage error formula or estimate to an exact value. See percentage change, difference and error for other options. How to Calculate Here is the way to calculate a percentage error: Step 1: Calculate the error (subtract one http://spiff.rit.edu/classes/phys273/uncert/uncert.html value form the other) ignore any minus sign. Step 2: Divide the error by the exact value (we get a decimal number) Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign) As A Formula This is the formula for "Percentage Error": |Approximate Value − Exact Value| × 100% |Exact Value| (The "|" symbols mean https://www.mathsisfun.com/numbers/percentage-error.html absolute value, so negatives become positive) Example: I thought 70 people would turn up to the concert, but in fact 80 did! |70 − 80| |80| × 100% = 10 80 × 100% = 12.5% I was in error by 12.5% Example: The report said the carpark held 240 cars, but we counted only 200 parking spaces. |240 − 200| |200| × 100% = 40 200 × 100% = 20% The report had a 20% error. We can also use a theoretical value (when it is well known) instead of an exact value. Example: Sam does an experiment to find how long it takes an apple to drop 2 meters. The theoreticalvalue (using physics formulas)is 0.64 seconds. But Sam measures 0.62 seconds, which is an approximate value. |0.62 − 0.64| |0.64| × 100% = 0.02 0.64 × 100% = 3% (to nearest 1%) So Sam was only 3% off. Without "Absolute Value" We can also use the formula without "Absolute Value". This can give a positive or negative result, which may be useful to know. Approximate Value − Exact Value × 100% Exact Value Example: They
Support Answers MathWorks Search MathWorks.com MathWorks Answers Support MATLAB Answers™ MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak https://www.mathworks.com/matlabcentral/answers/22066-calculating-and-adding-percent-error-to-a-graph Anniversary Home Ask Answer Browse More Contributors Recent Activity Flagged Content http://www.thestudentroom.co.uk/showthread.php?t=191290 Flagged as Spam Help MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak Anniversary Home Ask Answer Browse More Contributors Recent Activity Flagged Content Flagged as Spam Help Trial software Karen (view profile) 5 questions 0 answers 0 accepted answers Reputation: 0 percentage error Vote0 Calculating and Adding Percent Error to a Graph Asked by Karen Karen (view profile) 5 questions 0 answers 0 accepted answers Reputation: 0 on 23 Nov 2011 Accepted Answer by Fangjun Jiang Fangjun Jiang (view profile) 11 questions 1,712 answers 696 accepted answers Reputation: 3,933 160 views (last 30 days) 160 views (last 30 days) The Percent Error adding percentage error = 100*abs(exact solution-Approximate solution)/Exact Solution. I am writing a Euler method approximation and I need to know how best to present this. I keep getting the error message that "matrix dimensions must agree". Here is my code.%Script that demonstrates Euler integration for a first order problem using %MATLAB. %The problem to be solved is: %y'(t)+2*y(t)=2-exp(-4*t) %This problem has a known exact solution %y(t)=1+0.58*exp(-4*t)-0.5*exp(-2*t) function ystar = Eulermethod20(n) a=0; b=5; h=(b-a)/n; t=0:h:5;%Initialize time variable clear ystar;%wipe out old variable ystar(1)=1.0;%Initial condition (same for approximation) for i=1:length(t)-1, %Set up "for" loop k1=2-exp(-4*t(i))-2*ystar(i); %Calculate the derivative ystar(i+1)=ystar(i)+h*k1;%Estimate new value of y end %Exact solution y=1+0.5*exp(-4*t)-0.5*exp(-2*t);%Plot approximate and exact solutions plot(t,ystar,'b--',t,y,'r-'); legend('Approximate','Exact'); title('Euler Approximation'); xlabel('Time'); ylabel('y*(t), y(t)'); percent_error= 100*(1)+(0.5*exp(-4*t)-(0.5*exp(-2*t))-(2-exp(-4*t(i)))-(2*ystar(i))/((1)+(0.5*exp(-4*t))-(0.5*exp(-2*t)))); legend('Percent Error') The program runs, but the percent error doesn't calculate correctly. I need to calculate and show the error for this project and I was hoping someone can help. Thanks! 2 Comments Show all comments Fangjun Jiang Fangjun Jiang (view profile) 11 questions 1,712 answers 696 accepted answers Reputation: 3,933 on 23 Nov 2011 Direct link to
Anglia Ruskin University University of the Arts London (UAL) Aston University Bangor University University of Bath Bath Spa University University of Bedfordshire University of Birmingham Birmingham City University University of Bolton Bournemouth University BPP University University of Bradford University of Brighton University of Bristol Brunel University University of Buckingham Buckinghamshire New University University of Cambridge Canterbury Christ Church University Cardiff Metropolitan University Cardiff University University of Central Lancashire (UCLan) University of Chester University of Chichester City University London Coventry University University of Cumbria De Montfort University University of Derby University of Dundee Durham University University of East Anglia (UEA) University of East London Edge Hill University University of Edinburgh Edinburgh Napier University University of Essex University of Exeter Falmouth University University of Glasgow Glasgow Caledonian University University of Gloucestershire Glynd?r University Goldsmiths University University of Greenwich Heriot-Watt University University of Hertfordshire University of Huddersfield University of Hull Imperial College, London Keele University University of Kent King's College London Kingston University Lancaster University University of Leeds Leeds Metropolitan University Leeds Trinity University University of Leicester University of Lincoln University of Liverpool Liverpool Hope University Liverpool John Moores University London Metropolitan University London School of Economics London South Bank University Loughborough University University of Manchester Manchester Metropolitan University (MMU) Middlesex University University of Newcastle New College of the Humanities University of Northampton Northumbria University University of Nottingham Nottingham Trent University Open University University of Oxford Oxford Brookes University University of Plymouth University of Portsmouth Queen Margaret University Queen Mary, University of London Queen's University Belfast University of Reading Robert Gordon University University of Roehampton Royal Holloway University of Salford University of Sheffield Sheffield Hallam University SOAS, University of London University of South Wales University of Southampton Southampton Solen