Calculating Error for Measuring y3 in Range x1 to x2

[Doctor Luz]

Suppose I have some measures of certain physical magnitude "I" between the range x=x1 and x=x2.

I have for each x in this range a value y of I, then y=I(x)

I have a continuous level of noise y=y1.

I have I(x3)=y3 with x1<=x3<=x2.

how can I compute the error measuring y3?

Thank you

 

[HallsofIvy]

If I read this correctly then I(x) is a function of x for x between
x1 and x2. You then say "I have a continuous level of noise y=y1."
That's a bit confusing. Is y1 a constant? Since you had already used y to represent the value of the function I(x), do you intend y1 to be a noise on the value of I(x) or on x itself? I doubt that you intend the former since that in that case the answer would be, of course, y1. If you intend the latter, then, since relationship between the error in x and the error in y= I(x) depends heavily upon the function I, there is no general formula.

 

[tacman]

for sharing this question. Calculating error for measuring y3 in the range x1 to x2 involves considering the accuracy and precision of the measurements taken. To compute the error, we can use the following formula: error = y3 - I(x3). This measures the difference between the expected value of y3 and the actual measured value of y3.

Additionally, we can also calculate the percentage error by using the formula: (error / y3) * 100. This will give us the percentage of the error in relation to the expected value of y3.

However, it is important to note that the accuracy and precision of the measurements can greatly affect the error calculation. If the measurements are not accurate, the error will be larger, and if the measurements are not precise, the error will be more spread out. Therefore, it is crucial to ensure that the measurements taken are as accurate and precise as possible to minimize error.

Furthermore, it is also important to consider the level of noise (y=y1) in the measurements. This can be accounted for by using statistical methods such as standard deviation or confidence intervals to evaluate the reliability of the data and determine the margin of error.

In conclusion, calculating error for measuring y3 in the range x1 to x2 involves considering the accuracy and precision of the measurements, as well as accounting for any noise in the data. By using appropriate formulas and statistical methods, we can determine the error and its impact on the measured value of y3.