Error Calculation Constant
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Error and Root Mean Square Error -Labview June 19, 2008 by vennilakrishnan Imagine a target where archer A and archer B are trying their luck for a good shot. The following figure is the outcome. Now let us try to figure out who has done error calculation physics the best. Again it depends on what you want to see. The common error
Error Calculation Chemistry
measurements are as follows: Â Â Â Â Â Â Â Â Â Â Constant Error: Â Constant error measures the deviation
Standard Error Calculation
from the target. The formula for it is: Σ (xi-T)/N, where T is the target and N is the number of shots. It comes with a positive or negative sign which points out the direction
Relative Error Calculation
of the error. Absolute constant error will give the absolute value of CE alone without mentioning the direction.  Variable Error :  Variable error measures the consistency of the shots. It calculates the standard deviation of the total shots. Its formula is sq.root (Σ (xi-M)^2/N, where M is the average shot.  Absolute Error: Absolute error is the overall deviation without considering the direction. In constant error there is a danger of error calculation division cancellations of error because of direction. However, the error due to bidirection gets eliminated in absolute error. Its formula is Σ absolute ((xi-T)/N).         So here is a question for you? Among A and B, who is the better archer? Are you bothered about the deviationper se or concerned more about the consistency? I would say bet on archer B than A because he has lesser variablity. Root Mean Square Error:  This measures both the deviation and the consistency of the shots. Its formula is sq.root (Σ (xi-T)2/N).     Coefficient of Variation: It is nothing but standard deviation divided by mean. It gives a clear picture about the deviation. If there are lots of tremors, then the standard deviation increases and so the coefficient of variation. Check: Constant Error, Variable Error, Absolute Error & Root Mean Square Error Ref: Richard A. Schmidt, Timothy D Lee, (1999. Motor Control and Learning (Third Edition). Human Kinetics. Click on the image to get a close-up view! The explanations about all the errors are here. Click the link below. Measurements of Error Like this:Like Loading... Related Posted in Labview | 1 Comment One Response on September 22, 2009 at 2:05 pm | Reply Mehmet Thanks Vennila.
find that the error in this measurement is 0.001 in. To find the area we multiply the width (W) and length (L). The area then is L x W = (1.001 in) x (1.001 in) = 1.002001 in2 which experimental error calculation rounds to 1.002 in2. This gives an error of 0.002 if we were given that percentage error calculation the square was exactly super-accurate 1 inch a side. This is an example of correlated error (or non-independent error) since the error in percent error calculator L and W are the same. The error in L is correlated with that of in W. Now, suppose that we made independent determination of the width and length separately with an error of 0.001 in each. In this https://motorcontrol.wordpress.com/2008/06/19/constant-error-variable-error-absolute-error-and-root-mean-square-error-labview/ case where two independent measurements are performed the errors are independent or uncorrelated. Therefore the error in the result (area) is calculated differently as follows (rule 1 below). First, find the relative error (error/quantity) in each of the quantities that enter to the calculation, relative error in width is 0.001/1.001 = 0.00099900. The resultant relative error is Relative Error in area = Therefore the absolute error is (relative error) x (quantity) = 0.0014128 x 1.002001=0.001415627. which rounds to http://www.utm.edu/~cerkal/Lect4.html 0.001. Therefore the area is 1.002 in2± 0.001in.2. This shows that random relative errors do not simply add arithmetically, rather, they combine by root-mean-square sum rule (Pythagorean theorem). Let’s summarize some of the rules that applies to combining error when adding (or subtracting), multiplying (or dividing) various quantities. This topic is also known as error propagation. 2. Error propagation for special cases: Let σx denote error in a quantity x. Further assume that two quantities x and y and their errors σx and σy are measured independently. In this case relative and percent errors are defined as Relative error = σx / x, Percent error = 100 (σx / x) Multiplying or dividing with a constant. The resultant absolute error also is multiplied or divided. Multiplication or division, relative error. Addition or subtraction: In this case, the absolute errors obey Pythagorean theorem. If a and b are constants, If there are more than two measured quantities, you can extend expressions provided above by adding more terms under the square root sign. Square or cube of a measurement : The relative error can be calculated from where a is a constant. Example 1: Determine the error in area of a rectangle if the length l=1.5 ±0.1 cm and the width is 0.42±0.03 cm. Using the rule for multiplication
would be your guess: can an American Corvette get away if chased by an Italian police Lamborghini?
The top speed https://phys.columbia.edu/~tutorial/propagation/tut_e_4_3.html of the Corvette is 186 mph ± 2 mph. The top speed of the Lamborghini Gallardo is 309 km/h ± 5 km/h. We know that 1 mile = 1.61 km. In order to convert the speed of the Corvette to km/h, we need to multiply it by the factor of 1.61. What should we do with the error? Well, you've learned in the previous section that error calculation when you multiply two quantities, you add their relative errors. The relative error on the Corvette speed is 1%. However, the conversion factor from miles to kilometers can be regarded as an exact number.1 There is no error associated with it. Its relative error is 0%. Thus the relative error on the Corvette speed in km/h is the same as it was in mph, 1%. (adding error calculation constant relative errors: 1% + 0% = 1%.) It means that we can multiply the error in mph by the conversion constant just in the same way we multiply the speed. So our answer for the maximum speed of the Corvette in km/h is: 299 km/h ± 3 km/h. Now we are ready to answer the question posed at the beginning in a scientific way. The highest possible top speed of the Corvette consistent with the errors is 302 km/h. The lowest possible top speed of the Lamborghini Gallardo consistent with the errors is 304 km/h. Bad news for would-be speedsters on Italian highways. No way can you get away from that police car. The rule we discussed in this chase example is true in all cases involving multiplication or division by an exact number. You simply multiply or divide the absolute error by the exact number just as you multiply or divide the central value; that is, the relative error stays the same when you multiply or divide a measured value by an exact number. << Previous Page Next Page >> 1 For this example, we are regarding the conversion 1 mile = 1.61 km as e