Statistics: sample median, means, s.d. vs sample size

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SUMMARY

The discussion centers on the relationship between sample size and the standard deviation (SD) of sample statistics, specifically medians, means, and standard deviations. The user conducted an experiment with a dataset of 10,000 entries, taking 1,000 samples of sizes 4, 16, 64, and 1024, and graphed the SD of medians, means, and standard deviations against sample size using R. The user concluded that the formula SD of sample means = population SD / sqrt(sample size n) appears to apply similarly to medians and standard deviations, prompting a request for validation of this observation.

PREREQUISITES
  • Understanding of statistical concepts such as sample size, means, medians, and standard deviations.
  • Familiarity with the Central Limit Theorem and its implications for sample statistics.
  • Proficiency in R programming for statistical analysis and graphing.
  • Knowledge of population versus sample statistics and their relationships.
NEXT STEPS
  • Research the application of the Central Limit Theorem to medians and standard deviations.
  • Explore R's statistical functions for calculating means, medians, and standard deviations.
  • Investigate the implications of sample size on the accuracy of statistical estimates.
  • Learn about bootstrapping techniques for estimating the distribution of sample statistics.
USEFUL FOR

Statisticians, data analysts, and researchers interested in understanding the behavior of sample statistics in relation to sample size and the implications for data analysis using R.

jhson114
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i have a set containing 10000 data. i took 1000 samples of size 4, 16, 64, and 1024 and took the medians, means, and stadard deviations of each size. i graphed them sd of medians vs sample size, sd of mean vs sample size, and sd of s.d. vs sample size. for sample mean, i know from a textbook that:
SD of sample means = population SD / sqrt(sample size n).
But it seems from the graph i created using R, sd of medians and s.d. vs sample size all have the exact same looking graph, which to me suggests that:
SD of sample means, medians, and s.d. = population SD / sqrt(sample size n).
Is this right? it seems a little awkward. any input will be very helpful. thank you
 
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graph i created using R
What is R?

More generally, is your question whether the "sample vs. population" formula (sample stat = population stat/sqrt(n)) applies to median and std. dev. in addition to the mean?
 
R is just a program language kind of like matlab.

"More generally, is your question whether the "sample vs. population" formula (sample stat = population stat/sqrt(n)) applies to median and std. dev. in addition to the mean?"

This is exact what I'm asking.
 

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