Reconstructing dataset given mean, median and Stdev

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SUMMARY

It is possible to reconstruct an approximate dataset given the mean, median, standard deviation, and sample size (N). In the discussed example, with 20 students, a mean of 80, a median of 85, a standard deviation of 14, and a known score of 96, various datasets can satisfy these conditions. The challenge lies in the underdetermined nature of the problem, as multiple datasets can yield the same statistical properties. Techniques such as optimization and simulation can be employed to generate feasible datasets that adhere to the specified constraints.

PREREQUISITES
  • Understanding of basic statistics (mean, median, standard deviation)
  • Familiarity with dataset reconstruction techniques
  • Knowledge of optimization methods
  • Experience with statistical software or programming languages (e.g., Python, R)
NEXT STEPS
  • Explore methods for dataset reconstruction using statistical properties
  • Learn about optimization techniques in Python (e.g., SciPy library)
  • Investigate Monte Carlo simulations for generating datasets
  • Study the implications of constraints in statistical modeling
USEFUL FOR

Statisticians, data scientists, and researchers involved in data analysis and reconstruction, particularly those working with incomplete datasets or statistical modeling.

ruberhelios
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Wondering if it is possible to reconstruct a dataset if I give you the mean, median, standard deviation and N of a dataset.

For example, if there are 20 students in a class. The mean of their exam score is 80, median is 85, standard deviation is 14. Of course the maximum score for the exam can only be 100 and minimum zero. I can also further tell you that one student got 96.

Is there a way to reconstruct an approximate dataset to reflect these conditions? Thanks for your attention!
 
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In the abstract you have 20 variables and only a few equations, so there are many possible solutions.
 

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