Please submit your concern

Explanation:

The known observations are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29

Median of all 13 observations is 12, hence there must be 6 values greather than or equal to 12 and 6 values less than or equal to 12.

We see that for known observations, we already have 6 values (16, 19, 21, 21, 27 and 29) which are greather than 12. Hence, both the unknown values i.e., A and B must be less than 12.

Also, the smallest of these observations is 2 (given) and we know A < B, hence A = 2.

The lowest 6 observations are 2, 5, 6, 7, 8 and B.
The lower hinge is 6.5. Hence, B should take a value such than 6 and 7 are the middle two numbers when arranged in ascending order.
This is possible when B is greater than or equal to 7 and less than or equal to 12.

∴ Possible values of B are 7, 8, 9, 10, 11 or 12.

Hence, option (c).