JAMB 1998 · UME · Q44

Find the variance of the numbers $K$ , $K + 1$ , $K + 2$ .

Worked solution (try it first)

The three numbers add up to $3K + 3$ , so the mean is $\frac{3K + 3}{3} = K + 1$ .
The deviations are $-1$ , 0 and 1, so the squared deviations add up to 2.
The variance is $\frac23$ , option A.
It does not depend on $K$ .