The table below shows the distribution of marks scored by students in a class test. If the median mark is 4, find the value of x. Mark: 2, 3, 4, 5, 6 Frequency: 3, x, 5, 4, 2

The total frequency is 3 + x + 5 + 4 + 2 = 14 + x. For the median to be 4, the middle value(s) must fall in the class with mark 4. The cumulative frequency up to mark 3 is 3 + x, and up to mark 4 is 8 + x. For the median (the ((14+x)/2)th value) to be 4, we need 3 + x < (14+x)/2 ≤ 8 + x. Solving 3 + x < (14+x)/2 gives 6 + 2x < 14 + x, so x < 8. Testing x = 6: total = 20, median position = 10th value; cumulative up to mark 3 = 9, up to mark 4 = 14, so the 10th value is 4. This confirms x = 6.