F.3 Math (find unknown data )

The median of four numbers 62, 56, 73 and c is 61.
Consider sorting the three known numbers first. 56 < 62 < 73
If c ≤ 56, the median would be (56+62)/2 = 59, which is not true.
If c > 62, the median would be greater than 62, which is not true.
Therefore, we know that 56 < c ≤ 62.
In other words, the ordering of all four numbers is:

56 < c ≤ 62 < 73

Then, the median is (c+62)/2 = 61

c + 62 = 122

c = 60

Since there are 4 numbers altogether, so there must be 2 numbers below the median and 2 numbers above the median and the average of the middle 2 numbers is the median. Now the median is 61 and there are already 2 numbers above it ( 62 and 73), so c must be smaller than 61. Also, the average of 56 and 62 is not 61, that means 61 must be the average of c and 62.
That is (c + 62)/2 = 61 , thus c = 122 - 62 = 60.