Since x + y = 100, the total cumulative frequency at the last row must be 100.

Median class = 30 – 40.

Median = L + \left( \frac{\frac{n}{2} - CF}{f} \right) \times h

where:

• L = 30
• n = 100 (total frequency)
• CF = 35 + x
• f = 30
• h = 10
• Median = 32

Substituting values:

32 = 30 + \left( \frac{50 - (35 + x)}{30} \right) \times 10

or, 32 – 30 = \left( \frac{15 - x}{30} \right) \times 10

or, 2 =   \frac{150 - 10x}{30}

or, 60 = 150 – 10x

or, 10x = 90

or, x = 9

Now, x + y = 100

or,9 + y = 100

y = 91

∴ x = 9 and y = 91