The deviations from the mean of a set of numbers are ((k+3)^{2}, (k+7), -2, text{k and (} k+2)^{2}), where k is a constant. Find the value of k.
-
A.
3 -
B.
2 -
C.
-2 -
D.
-3
Correct Answer: Option D
Explanation
The sum of deviations from the mean of a set of numbers equals 0.
((k+3)^{2} + (k+7) + (-2) + k + (k+2)^{2} = 0)
((k^2 + 6k + 9) + (k+7) – 2 + k + (k^2 + 4k + 4) = 0)
(2k^{2} + 12k + 18 = 0)
(2k^{2} + 6k + 6k + 18 = 2k(k + 3) + 6(k + 3) = 0)
(k = -3 (twice))