Question

If the median of the following distribution is 32.5, then find the values of x and y.

Hint:

Ensure you pick the cumulative frequency ($cf$) of the class PRECEDING the median class when applying the formula.

Answer 1

Step 1: Total Frequency Condition
Given total frequency n = 40

So,
x + 5 + 9 + 12 + y + 3 + 2 = 40

x + y + 31 = 40
x + y = 9 …(1)

Step 2: Identify Median Class
n/2 = 40/2 = 20

Median = 32.5
So median class = 30 − 40

For median class:
l = 30
f = 12
h = 10
cf (before median class) = x + 14

Step 3: Apply Median Formula
Median = l + [(n/2 − cf)/f] × h

32.5 = 30 + [(20 − (x + 14))/12] × 10

2.5 = [(6 − x)/12] × 10

Multiply both sides by 12:
2.5 × 12 = (6 − x) × 10
30 = 10(6 − x)

3 = 6 − x
x = 3

Step 4: Find y
From equation (1):
3 + y = 9
y = 6

Final Answer:
x = 3
y = 6