Sample statistics vs population statistics

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SUMMARY

The discussion centers on the differences between sample statistics and population statistics, specifically addressing the calculations of sample mean (x̄), sample standard deviation (s), population mean (µ), and population standard deviation (σ). The participants highlight that the non-normal distribution invalidates the empirical rule and emphasize the Central Limit Theorem, which states that larger sample sizes yield means closer to the population mean. The conversation concludes that sample statistics are estimations of population parameters, and discrepancies arise due to the inherent variability in sampling.

PREREQUISITES
  • Understanding of Central Limit Theorem
  • Knowledge of statistical measures: mean (x̄, µ) and standard deviation (s, σ)
  • Familiarity with concepts of sampling and population statistics
  • Awareness of distribution types and their implications on statistical analysis
NEXT STEPS
  • Study the implications of non-normal distributions on statistical analysis
  • Explore the Central Limit Theorem in depth
  • Learn about sampling techniques and their impact on data accuracy
  • Investigate methods for estimating population parameters from sample statistics
USEFUL FOR

Students in statistics, data analysts, and researchers who need to understand the relationship between sample and population statistics and the impact of sample size on statistical inference.

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Homework Statement



My task is to explain why the sample statistics I have obtained differ from the population statistics I have obtained from some data - using "concepts taught in class, if they exist". I have calculated x̄ and s, as well as σ and µ.

Homework Equations



First of all, the distribution is not normal, thus the emperical rule is invalid.

The Attempt at a Solution



Part of me thinks it's a trick question because there are very few "concepts" I can think of. The only thing I can come up with is that the mean differs because it is merely one sample, and according to the Central Limit Theorum, if I had a bigger sample space, the mean would be similar. Similarly, the standard deviation differs because it is merely one sample. Is this all there is to it or am I missing something?
 
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Sample statistics are obtained by sampling from a population. The idea is that the statistical properties of a population can (usually) be only estimated. In this respect, I slightly doubt about your data-based [itex]\mu, \sigma^2[/itex] :-)
 

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