The marks of eight students in a Hindi test, in ascending order, are 42, 47, 51, $x$, $x + 4$, 63, 68 and 71. The median mark is 56. What is $x$?

Explanation

1. 01

   With 8 values the median is the average of the 4th and 5th: $\frac{x + (x + 4)}{2} = 56$.

2. 02

   So $2x + 4 = 112$, giving $2x = 108$ and $x = 54$.

3. 03

   Check: the list 42, 47, 51, 54, 58, 63, 68, 71 is still in order.