JAMB 2000 · UME · Q47

Dispersion & cumulative frequency

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

Worked solution (try it first)

The five numbers add up to $15x$ , so the mean is $\frac{15x}{5} = 3x$ .
The deviations are $-2x$ , $-x$ , 0, $x$ , $2x$ .
Their squares add up to $4x^2 + x^2 + 0 + x^2 + 4x^2 = 10x^2$ .
The variance is $\frac{10x^2}{5} = 2x^2$ , option B.

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