中心極限定理を巡って : Tスコアーの教育的有効性

概要

論文の詳細を見る
The function f:x→e^<-x2>(-∞<x<∞) representing a symmetrical hanging graph about the straight line x=0 is ⎰^∞_<-∞e^<-x2>dx=√<π>. It deduces the continuous variable Z probability density function p(z)=e^<-x^2/2>/√<2π>(-∞<z<∞) according to N(0,1^2), the standard normal distribution. I deduce the variable X probability density function f(x)=e<-(x-m)^2/2σ^2/√<2π>σ(-∞<x<∞), (σ>o) according to N(m, σ^2), the normal distribution from the relation between the continuous variable Z probability density function and the discrete variable X probability density function pn(x)=_nC_xp^x(1-p)^<n-x> (x=0,l,2,…,n), (0≩p≩1) according to the binominal distribution. Using these functions, I analyze the Z-score : z=(x-x^^-)/s which is used as the standardized raw score in the fields of pedagogy and psychology nowadays and the T-score: t=50+10(x-x^^-)/s which is ofen used at lessons as the practical application on the basis of the central limit theorem lim__<n→∞>P(α≨√<n>(x^^--μ)/δ≨β)=⎰^β_ap(z)dz (μ:population mean, δ:population variance and x^^-:sample mean) consisting in the connection betwoon the population and the sample. I conclude by considering the mathematical significance and educational efficiency for the practical application.
名古屋女子大学の論文
1989-03-10