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The deviations from the mean of a set of numbers are \((k+3)...

The deviations from the mean of a set of numbers are (k+3)2,(k+7),2,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 is D

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

(k2+6k+9)+(k+7)2+k+(k2+4k+4)=0

2k2+12k+18=0

2k2+6k+6k+18=2k(k+3)+6(k+3)=0

k=3(twice)