C? Not sure if this is correct

Q: Is SD (A) > SD (B)?

1) Difference between ages of any two is always > 1. To get the smallest possible SD for A, we can assume:

8 students have age = 14.5

8 students have age = 15.5 (which still makes mean = 15)

Smallest possible SD(A)^2 = [16* (deviation of each number from mean)^2]/16

= 12 * 0.5^2/16 = 0.5^2

=>Smallest possible SD(A) = 0.5

No information on ages of ClassB. INSUFF.

2) Difference between ages of any two is always < 0.5 (6 months). To get the largest possible SD we can assume:

6 students have age = 11.75

6 students have age = 12.25 (mean is still 12)

=> The largest possible SD(B) = 0.25

No information about classA. INSUFF.

Combining 1 & 2:

Since the smallest possible SD(A) is greater than the largest possible SD(B) it must be true that

Hence SD(A) > SD(B)

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