Question 46

Jambmaths question: 

The variance of x, 2x, 3x, 4x and 5x is

Option A: 

$x\sqrt{2}$

Option B: 

3x

Option C: 

x2 

Option D: 

2x2

Jamb Maths Solution: 

$\begin{align}  & mean=\overline{x}=\frac{x+2x+3x+4x+5x}{5}=\frac{15x}{5}=3x \\ & variance={{\sigma }^{2}} \\ & {{\sigma }^{2}}=\frac{{{\left| x-3x \right|}^{2}}+{{\left| 2x-3x \right|}^{2}}+{{\left| 3x-3x \right|}^{2}}+{{\left| 4x-3x \right|}^{2}}+{{\left| 5x-3x \right|}^{2}}}{5} \\ & {{\sigma }^{2}}=\frac{4{{x}^{2}}+{{x}^{2}}+0+{{x}^{2}}+4{{x}^{2}}}{5}=\frac{10{{x}^{2}}}{5}=2{{x}^{2}} \\\end{align}$

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