The median of the given set {3, 5, 7, 2k, 12, 16, 21, 24} arranged in ascending order is 11.
To find the median, we first arrange the given set in ascending order:
3,5,7,2k,12,16,21,24.
Since the mean deviation about the median is given as 6, we know that the median is 6 units away from the other values on average. The mean deviation is calculated using the formula:
Mean Deviation = Σ|xi - median|/n
For this set, the sum of mean deviations is 6×8=48. Since there are four values below the median and four values above the median, the median must be the average of the fourth and fifth terms in the ordered set. The fourth term is 2k, and the fifth term is 12. The average of these two values is (2k+12)/2, and we set this equal to the mean deviation (48) to solve for k:
(2k+12)/2=48
2k+12=96
2k=84
k=42
Now that we know the value of k is 42, we substitute it back into the ordered set and find the median:
Ordered Set: 3,5,7,42,12,16,21,24
The median is the average of the fourth and fifth terms: (7+12)/2=11. Therefore, the correct answer is D. 11.