X, 3, 1, 12, 8 if x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

Solution:

If X is the median then it should be in the middle of the sequence:

1, 3, X, 8, 12

The average of the 5 numbers is given as :

Average = (1 + 3 + X + 8 + 12)/5

= (24 + X)/5

Now X (Median) is an integer which is greater than average of the five numbers

Therefore

X > (24 + X)/5

5X > 24 + X

4X > 24

X > 6

Since X is an integer and the median of the above sequence the only value it can take is X = 7

X, 3, 1, 12, 8 if x is an integer, is the median of the 5 numbers shown greater than the average (arithmetic mean) of the 5 numbers?

Summary:

In the sequence X, 3, 1, 12, 8 if x is an integer, and it is the median of the 5 numbers shown and greater than the average (arithmetic mean) of the 5 numbers then the value of X = 7