How to correctly average over multiple data sets

[knowlewj01]

Homework Statement

In a particular Magneto-Optic Kerr Effect (MOKE) experiment I have taken data for 20 hysteresis loops in which Kerr Voltage is measured as a function of Applied Field. I wish to obtain an average curve. The problem is this; Even though the settings for each loop were identical (magnetic field set to scan the range ±150 Oe in steps of 2 Oe), the recorded data for the applied field differ slightly between loops and the step size isn't always exactly 2Oe. How should I average them?

Homework Equations

The Attempt at a Solution

To start with, I cut the data down so it's in the range ±60 Oe (Past this point it is saturated so no more changes occur). I made sure the starting point for the field was in roughly the same point (about 59.5±0.5 Oe). Then I took the avg value and stdev of each successive data point (Field and Kerr Voltage). Is this an acceptable way of doing this? I thought about maybe binning the data into small bins, around 1Oe in size. Does anyone know what to do in this sort of situation?

 

[mark726]

Thank you for sharing your experimental setup and data analysis approach. It seems like you have already taken some good steps in trying to average your data. However, there are a few more things you can consider to improve the accuracy of your average curve.

Firstly, it is important to ensure that the variations in your applied field are not due to any external factors, such as temperature fluctuations or magnetic interference. If possible, try to control for these variables or repeat the experiment in a more controlled environment.

Secondly, instead of cutting the data down to a specific range, it may be more accurate to use all the data points and interpolate them onto a common grid. This will allow for a more precise comparison between the different hysteresis loops.

Additionally, instead of taking the average and standard deviation of each data point, you can try using a weighted average. This takes into account the variations in your applied field and assigns a higher weight to data points with smaller variations.

Lastly, binning your data into smaller bins can also help to smooth out any fluctuations and improve the accuracy of your average curve. However, be cautious of using bins that are too small, as this can lead to loss of information.

Overall, it is important to carefully consider the sources of variation in your data and use appropriate methods to account for them in your average curve. I hope this helps and good luck with your analysis.