Show how the variance decrease as degrees of freedom/sample size get bigger

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SUMMARY

The discussion centers on understanding how variance decreases as degrees of freedom and sample size increase, specifically using the formula V = (n-1)S²/σ², which follows a Chi-squared distribution with (n-1) degrees of freedom. Participants express confusion over obtaining larger variances instead of the expected decrease, indicating a misunderstanding of the variance formula for the Chi-squared distribution. Clarification on the relevance of a provided chart is also sought, highlighting the need for accurate interpretation of statistical tools.

PREREQUISITES
  • Understanding of variance and standard deviation concepts
  • Familiarity with Chi-squared distribution properties
  • Knowledge of sample size and degrees of freedom in statistics
  • Ability to interpret statistical charts and formulas
NEXT STEPS
  • Review the variance formula for the Chi-squared distribution
  • Study the relationship between sample size and variance reduction
  • Learn about the implications of degrees of freedom in statistical analysis
  • Examine practical examples of variance calculations in real datasets
USEFUL FOR

Students and professionals in statistics, data analysts, and anyone looking to deepen their understanding of variance behavior in relation to sample size and degrees of freedom.

rogo0034
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Homework Statement


TNtoZ.png



Homework Equations



XY0kG.png


The Attempt at a Solution



I'm confused actually how to go about this. Sounds very simple, but when i do what they suggest, 'first, find the variance of (n-1)s2/σ2

i get larger variances rather than smaller, which makes no sense. should i be using the chart for this? (below)

uhT2u.png
 
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rogo0034 said:

Homework Statement


TNtoZ.png



Homework Equations



XY0kG.png


The Attempt at a Solution



I'm confused actually how to go about this. Sounds very simple, but when i do what they suggest, 'first, find the variance of (n-1)s2/σ2

i get larger variances rather than smaller, which makes no sense. should i be using the chart for this? (below)

uhT2u.png

Since you don't tell us what the chart represents, it is impossible to tell if it is relevant or not; I suspect not.

You are told that V = (n-1)S^2/\sigma^2 has a Chi-squared distribution with (n-1) degrees of freedom. Do you know the variance formula for the Chi-squared distribution? (It is readily available.)

RGV
 

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