chapter 1

Chapter 1: Overview and Descriptive Statistics79.a.b.n+i=1 n[ nxn+ xnxi= ∑ xi+ xn+1 = nxn+ xn+1,soxn+1 =1 i=1( n + 1)∑ns=2n+1n∑i=1=x2in+1∑i=1= ( n −1)s( x − x−nx2n+i2n+ x2 22{ x + nx −(n + 1) x }n+1n+1)2n+12=+ nxnn+1∑i=12nx2i−(n + 1) x−(n + 1) xn+12n+12n+1+ 1]When the expression for xn+ 1from a is substituted, the expression in braces simplifies tothe following, as desired:n(xn+1− xn)( n + 1)215(12.58) + 11.8200.5c. x == 12. 53sn+ 1=16 162n −12 ( xn1− xn)14sn+= .512n ( n + 1) 152( ) ( )2+n + 1=(11.8 −12.58)+(16)= . 245+.038 = .238 . So the standard deviation s = .238 . 5322n+ 1=43