How Do You Calculate Error with a Single Measurement in Physics Lab Reports?

[Derik]

I'm currently in first year engineering and I seem to be struggling with Physics, which is not unlikely uncommon. A simple problem I've come across is not doing correct error analysis when writing up lab reports. In my current lab, which is justifying the relationship of angular frequency, force, mass and radius in centripetal motion, a portion of the questions ask to analyze different sources of random error; one of which being random error related to the mass. Since I didn't take multiple measurements of the same mass, how would I go about finding a mean and standard deviation? It doesn't make any sense to me to compare masses of two completely different apparatus setups, so am I looking at the problem wrong or did I just make an error by not taking multiple measurements (which the lab specifically says to do when it's required)?

Would really appreciate the help and can definitely go more in depth or even supply some lab data if it's required.

Thanks

Edit: Disregard the picture, too long of a story to explain :^)

 

[Dale]

Since I didn't take multiple measurements of the same mass, how would I go about finding a mean and standard deviation?

Hi Derik, welcome to PF!

The only other way I know is to look into the documentation of the measuring device and hope that the manufacturer tested and reported the device's measurement error.

 

[Derik]

Hi Derik, welcome to PF!

The only other way I know is to look into the documentation of the measuring device and hope that the manufacturer tested and reported the device's measurement error.

I do in fact have measurement errors, but how would I derive the random error using standard deviation?

 

[Dale]

I do in fact have measurement errors, but how would I derive the random error using standard deviation?

The standard deviation of the measurement is the "random error" of the measurement.

If you have to perform any computations using the measured value then you can estimate the standard deviation of the computed value through the propagation of errors.

 

[Derik]

The standard deviation of the measurement is the "random error" of the measurement.

If you have to perform any computations using the measured value then you can estimate the standard deviation of the computed value through the propagation of errors.

I mis-worded that. I do understand that the standard deviation of the measurement is the random error, but I'm wondering how I'm actually supposed to calculate it (as easy at that sounds). Let's say for example that my mass measurements have an uncertainty of +/- 0.05g and the measurement is arbitrarily 100g, a second measurement using a different apparatus setup is 200g +/- 0.05g. I know the equations used to find the standard mean, standard deviation and the deviation from mean, but I don't know how to do it with a single measurement. For example, I calculated the standard deviation from mean for my angular frequency; the difference is that I had 3 measurements for the same test.

 

[Dale]

I don't know how to do it with a single measurement.

You can't. The standard deviation for a single measurement is undefined.