If the sample size increases, what will happen to the standard deviation?

Dorsheele0p 2022-08-10 Answered
If the sample size increases, what will happen to the standard deviation?
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Answers (1)

Hamza Conrad
Answered 2022-08-11 Author has 20 answers
This is the practical reason for taking as large of a sample as is practical. For any given amount of 'variation' between measured and ‘true’ values (we can’t make that better in this scenario) increasing the sample size "N" at least gives us a better (smaller) standard deviation.
s = 1 N 1 i = 1 N ( x i x ¯ ) 2
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Euclid's view and Klein's view of Geometry and Associativity in Group
One common item in the have a look at of Euclidean geometry (Euclid's view) is "congruence" relation- specifically ""congruence of triangles"". We recognize that this congruence relation is an equivalence relation
Every triangle is congruent to itself
If triangle T 1 is congruent to triangle T 2 then T 2 is congruent to T 1 .
If T 1 is congruent to T 2 and T 2 is congruent to T 3 , then T 1 is congruent to T 3 .
This congruence relation (from Euclid's view) can be translated right into a relation coming from "organizations". allow I s o ( R 2 ) denote the set of all isometries of Euclidean plan (=distance maintaining maps from plane to itself). Then the above family members may be understood from Klein's view as:
∃ an identity element in I s o ( R 2 ) which takes every triangle to itself.
If g I s o ( R 2 ) is an element taking triangle T 1 to T 2 , then g 1 I s o ( R 2 ) which takes T 2 to T 1 .
If g I s o ( R 2 ) takes T 1 to T 2 and g I s o ( R 2 ) takes T 2 to T 3 then h g I s o ( R 2 ) which takes T 1 to T 3 .
One can see that in Klein's view, three axioms in the definition of group appear. But in the definition of "Group" there is "associativity", which is not needed in above formulation of Euclids view to Kleins view of grometry.
Question: What is the reason of introducing associativity in the definition of group? If we look geometry from Klein's view, does "associativity" of group puts restriction on geometry?