Find the variance of the numbers k, k+1, k+2,
A
\(\frac{2}{3}\)
B
1
C
k + 1
D
(k + 1)2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
mean (x) = \(\frac{\sum x}{N}\)
= k + k + 1 + k + 3
= \(\frac{3k + 3}{3}\)
= k + 1
\(\begin{array}{c|c} X & (X -X) & (X -X)^2\\ \hline k & -1 & 1 \\ k + 1 & 0 & 0\\ k + 2 & 1 \\ \hline & & 2\end{array}\)
Variance (52) = \(\frac{\sum (x - x)^2}{N}\)
= \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #30749)