σ2=∑nxi2−(∑nxi)2 Variance of 2x1,2x2,…..,2xn=∑n(2xi)2−(∑n2xi)2=4[∑nxi2−(∑nxi)2]=4σ2 Statement 1 is true. A.M. of 2x1,2x2,……,2xn=n2x1+2x2+⋯+2xn=2(nx1+x2+⋯+xn)=2xˉ Statement 2 is false.
Let x1,x2,……,xn be n observations, and let x be their arithematic mean and σ2 be their variance. Statement 1: Variance of 2x1,2x2,……,2xn is 4σ2. Statement 2: Arithmetic mean of 2x1,2x2,…..,2xn is 4x.
Held on 30 Apr 2012 · Verified 6 Jul 2026.
Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is false
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