Can I use mean, median, minimum, maximum, standard deviation, population size, and single sample to generate statistically identical data?

After each exam, the professor provides the following information.

• Minimum Score
• [Arithmetic] Mean
• Median
• Maximum Score
• Standard Deviation

I also know what my score was as well as how many students took the exam.

Is there a known way to take this other information into account such that calculating the mean, median, minimum, st. deviation, and maximum of the resulting dataset is an exact match for the given actual mean, median, minimum, and maximum AND that my score is among the output dataset?

I know that I can use numpy.random.normal to generate random data that tends toward a given distribution, e.g., numpy.random.normal(loc=median_of_scores, scale=sigma_of_scores, size=num_of_scores), but that only tends toward the statistical parameters. Also, it doesn't take into account known pieces of information (my score, the median, the minimum score, and the maximum score). Adding my score, the minimum score, and the maximum score would further warp the randomly-generated data away from the known population numbers.

https://stackoverflow.com/questions/67013651/can-i-use-mean-median-minimum-maximum-standard-deviation-population-size-a April 09, 2021 at 08:52AM