Challenge: Analyze and Report Experimental Results
In physics, you often collect experimental data to test predictions or explore physical laws. Analyzing such data requires you to calculate results, estimate uncertainties, and present findings clearly using visualizations. This challenge will give you practice with the entire workflow: you will analyze a dataset from a physics experiment, propagate uncertainties, create plots with error bars, and generate a concise summary report, just as you would in a real laboratory setting.
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You are given a set of experimental measurements and their corresponding uncertainties. Your task is to perform a thorough analysis and visualization of these results by following the steps below:
- Use the provided
datalist for your measured values and theuncertaintieslist for their associated uncertainties. - Calculate the mean (average) of the values in the
datalist usingnumpy.mean. - Calculate the standard deviation of the values in the
datalist usingnumpy.stdwithddof=1to obtain the sample standard deviation. - Compute the mean of the
uncertaintieslist usingnumpy.meanto represent the average uncertainty of your measurements. - Calculate the propagated (total) uncertainty by combining the standard deviation and the mean uncertainty. Use the formula:
sqrt(std_dev**2 + mean_uncertainty**2), wherestd_devis the sample standard deviation andmean_uncertaintyis the mean of theuncertaintieslist. - Generate a plot of the measurements using
matplotlib.pyplot.errorbar, where:- The x-axis should represent the trial number (e.g., 1, 2, 3, ...).
- The y-axis should represent the measured values from
data. - Error bars should be drawn using the values from the
uncertaintieslist. - Add a horizontal dashed line at the mean value to indicate the average of the measurements.
- Label the x-axis as 'Trial' and the y-axis as 'Measured Value'.
- Add an appropriate title and legend to the plot.
- Construct a concise summary report as a string that includes:
- The mean value (rounded to two decimal places).
- The standard deviation (rounded to two decimal places).
- The propagated uncertainty (rounded to two decimal places).
- Print the summary report.
- Return the mean value, standard deviation, and propagated uncertainty as a tuple from your function.
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What kind of physics experiment data will I be analyzing?
Can you explain how to propagate uncertainties in this context?
How do I create plots with error bars for my data?
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In physics, you often collect experimental data to test predictions or explore physical laws. Analyzing such data requires you to calculate results, estimate uncertainties, and present findings clearly using visualizations. This challenge will give you practice with the entire workflow: you will analyze a dataset from a physics experiment, propagate uncertainties, create plots with error bars, and generate a concise summary report, just as you would in a real laboratory setting.
Swipe to start coding
You are given a set of experimental measurements and their corresponding uncertainties. Your task is to perform a thorough analysis and visualization of these results by following the steps below:
- Use the provided
datalist for your measured values and theuncertaintieslist for their associated uncertainties. - Calculate the mean (average) of the values in the
datalist usingnumpy.mean. - Calculate the standard deviation of the values in the
datalist usingnumpy.stdwithddof=1to obtain the sample standard deviation. - Compute the mean of the
uncertaintieslist usingnumpy.meanto represent the average uncertainty of your measurements. - Calculate the propagated (total) uncertainty by combining the standard deviation and the mean uncertainty. Use the formula:
sqrt(std_dev**2 + mean_uncertainty**2), wherestd_devis the sample standard deviation andmean_uncertaintyis the mean of theuncertaintieslist. - Generate a plot of the measurements using
matplotlib.pyplot.errorbar, where:- The x-axis should represent the trial number (e.g., 1, 2, 3, ...).
- The y-axis should represent the measured values from
data. - Error bars should be drawn using the values from the
uncertaintieslist. - Add a horizontal dashed line at the mean value to indicate the average of the measurements.
- Label the x-axis as 'Trial' and the y-axis as 'Measured Value'.
- Add an appropriate title and legend to the plot.
- Construct a concise summary report as a string that includes:
- The mean value (rounded to two decimal places).
- The standard deviation (rounded to two decimal places).
- The propagated uncertainty (rounded to two decimal places).
- Print the summary report.
- Return the mean value, standard deviation, and propagated uncertainty as a tuple from your function.
Рішення
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