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Parameter
The statistical characteristic that may be calculated on the basis of population values of the variate is called Parameter.
statistic
The statistical characteristic that may be calculated on the basis of sample values of the variate is called Statistic.
Standard deviation
Let there be a population regarding X taking k valuei.e. x1,x2,... xk with corresponding probabilityp1,p2,.....pk ; Σpi= 1Then, E(x)= Σki=1xi.piE(x2) =Σki=1xi2.pi Var(X)=E[X-E(X)]2=E(X2)−E2(X)S.D.(X)= +√Var(X)={E(X−E(X))2}1/2 It is denoted by the symbol σ. It is a measure of dispersion.
Standard Error
Let the parameter be θ, and the statistic used for it’s estimator beτAn estimatorτis said to be an unbiased estimator ofθ.If E(τ)=θThe variance obtained by taking from an unbiased estimator is called M.S.E. MSE(τ)=E(τ-θ)2,where(τ-θ) is called error.The S.D. obtained from sampling distribution of is called Standard Error. S.E. ofθi.e. S.E.(τ)=[E(τ-Θ)]1/2 It is dependent on sample size n it becomes negligible as n tends to infinity(∞) .
