Basic standard deviation calculation

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SUMMARY

The discussion focuses on the calculation of standard deviation (SD) in relation to counts and rates. It establishes that the SD of the total number of counts (n) is represented as √n, while the rate (r) is defined as n/t, where t is time. The derivation of the standard deviation involves the relationship Δn = (Δr)⋅t, leading to the conclusion that Δr can be expressed as √(n/t²). This mathematical framework clarifies the reasoning behind squaring the time in the denominator.

PREREQUISITES
  • Understanding of basic statistics, specifically standard deviation
  • Familiarity with the concepts of counts and rates in statistical analysis
  • Knowledge of algebraic manipulation and equations
  • Basic grasp of time as a variable in calculations
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  • Study the derivation of standard deviation formulas in statistics
  • Learn about the implications of rates in statistical calculations
  • Explore the application of standard deviation in real-world data analysis
  • Investigate the relationship between variance and standard deviation
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Students, statisticians, and data analysts seeking to deepen their understanding of standard deviation calculations and their applications in statistical analysis.

Graham87
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I don’t get how they got the equation for the standard deviation. Why do they only square with the time in the denominator?

Thanks!

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We know that the SD of the total number of counts n is √n and rate r =n/t

So;
n=rt
Δn = (Δr)⋅t =√(n/t)t
Δr=√(n)/t =√(n/t2)
 
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gleem said:
We know that the SD of the total number of counts n is √n and rate r =n/t

So;
n=rt
Δn = (Δr)⋅t =√(n/t)t
Δr=√(n)/t =√(n/t2)
Aha! Thanks!
 

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