What is the average of (Ri-1/N*Sum[Ri])^2 The sum is from i=1 to i=N.

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Homework Help Overview

The discussion revolves around the mathematical expression for the average of the squared deviation of a set of values, specifically focusing on the term (Ri - 1/N*Sum[Ri])^2, where the sum is taken from i=1 to i=N. Participants are exploring concepts related to averages, variance, and standard deviation in a statistical context.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the meaning of "Ri" and the expression for the average. Some are discussing the relationship between the average of squared deviations and variance, while others are questioning the familiarity of these concepts.

Discussion Status

There is an ongoing exploration of the mathematical relationships involved, with some participants providing definitions and context for variance and standard deviation. However, there is no explicit consensus on the interpretation of the original question or the symbols introduced.

Contextual Notes

One participant notes that the question involves proving a relationship between contour length and the radius of gyration, which introduces additional complexity to the discussion. There are indications of confusion regarding the symbols and terms used in the problem.

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What is the average of (Ri-1/N*Sum[Ri])^2 The sum is from i=1 to i=N.
 
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What is "Ri"?
 


Hi jaobyccdee! :smile:


1/N*Sum[Ri] is the average \bar R of R_i.

So you're asking about {1 \over N}\sum (R_i - \bar R)^2

Does that look familiar to you?
 


er...actually that's what i start with...but i don't know that it should be familiar...
 


The average of the deviation squared is called "variance".
Its square root is called "standard deviation".
 


Sorry, i should have mentioned that the question starts with sqrt<R^2>, and asks to prove that it is equal to sqrt(Lζ/3). This is the relationship between contour length and the radius of gyration. So i was trying to evaluate it to something that looks like sqrt(Na/6) where Na^2 is the variance.
 


jaobyccdee said:
Sorry, i should have mentioned that the question starts with sqrt<R^2>, and asks to prove that it is equal to sqrt(Lζ/3). This is the relationship between contour length and the radius of gyration. So i was trying to evaluate it to something that looks like sqrt(Na/6) where Na^2 is the variance.

I can't make chocolate of all these symbols you just introduced here...
 

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