Question

6 numbers from a list of 9 integers are 7, 8, 3, 5, 9 and 5 find the largest possible value of the median of all 9 numbers in this list

Answer 1

Arrange these six numbers in increasing order.

3,5,5,7,8,9 .

Let x, y, z be the remaining 3 numbers.

Case 1 :- The increasing order be x, 3,5,5,7,8,9,y,z .

Median = 5th term = 7 .

Case 2 :- The increasing order be x, y, 3,5,5,7,8,9,z

Median = 5term = 5 .

Case 3:- Let the increasing order be x, y, z, 3,5,5,7,8,9.

Median = 5th term = 5 .

Case 4 :- Let the increasing order be 3,5,5,7,8,9,x,y,z .

Median = 5th term = 8 .

Now, Possible medians = 5 , 7 , 8 [ not considering x, y, z as their values are unknown ]

5 < 7 < 8 .

8 is the highest possible median.

Therefore, the highest possible value of median = 8 .