Sample mean and sample covariance

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SUMMARY

The discussion focuses on the concepts of sample mean and sample covariance, specifically how observations can be structured into column vectors. Each observation is represented as a K × 1 column vector, where N denotes the number of observations and K the number of random variables. The user seeks clarification on these statistical concepts, indicating that resources like Wikipedia may not provide the necessary clarity. Alternative tutorials, such as those from Penn State, are recommended for a more concrete understanding.

PREREQUISITES
  • Understanding of random variables and their representations
  • Familiarity with statistical concepts such as sample mean and sample covariance
  • Basic knowledge of vector notation and matrix operations
  • Experience with statistical software or programming languages for data analysis
NEXT STEPS
  • Review the Penn State tutorial on sample mean and sample covariance
  • Explore statistical software like R or Python for practical applications
  • Study the mathematical derivation of sample mean and covariance
  • Learn about the implications of sample size on statistical estimates
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and students seeking to deepen their understanding of sample statistics and their applications in data analysis.

EnglsihLearner
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Let xij be the ith independently drawn observation (i=1,...,N) on the jth random variable (j=1,...,K). These observations can be arranged into N column vectors, each with K entries, with the K ×1 column vector giving the ith observations of all variables being denoted xi (i=1,...,N).


I have been reading the following link
http://en.wikipedia.org/wiki/Empirical_mean
to learn the Sample mean and sample covariance. But I am failing to understand the above part. Could someone please explain it to me in a easiest way?
 
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When a Wikipedia article is too schematic or abstract ... just do a search using the key words plus tutorial.
Then look over the articles found to find one that is more concrete such as this one:
https://online.stat.psu.edu/~ajw13/stat505/fa06/07_propmean/04_propmean_summary.htm
 

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