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Python for Physics Students

bookChallenge: 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.

Oppgave

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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 data list for your measured values and the uncertainties list for their associated uncertainties.
  • Calculate the mean (average) of the values in the data list using numpy.mean.
  • Calculate the standard deviation of the values in the data list using numpy.std with ddof=1 to obtain the sample standard deviation.
  • Compute the mean of the uncertainties list using numpy.mean to 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), where std_dev is the sample standard deviation and mean_uncertainty is the mean of the uncertainties list.
  • 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 uncertainties list.
    • 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.

Løsning

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Seksjon 3. Kapittel 7
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bookChallenge: Analyze and Report Experimental Results

Sveip for å vise menyen

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.

Oppgave

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 data list for your measured values and the uncertainties list for their associated uncertainties.
  • Calculate the mean (average) of the values in the data list using numpy.mean.
  • Calculate the standard deviation of the values in the data list using numpy.std with ddof=1 to obtain the sample standard deviation.
  • Compute the mean of the uncertainties list using numpy.mean to 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), where std_dev is the sample standard deviation and mean_uncertainty is the mean of the uncertainties list.
  • 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 uncertainties list.
    • 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.

Løsning

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Alt var klart?

Hvordan kan vi forbedre det?

Takk for tilbakemeldingene dine!

Seksjon 3. Kapittel 7
single

single

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