Let the missing frequencies be:
30–40 = a
40–50 = b
50–60 = c
Given:
Total frequency = 150
Median = 48.25
Mode = 44
Step 1: Using Total Frequency
3 + 7 + a + b + c + 20 + 16 + 4 = 150
50 + a + b + c = 150
⇒ a + b + c = 100 …(1)
Step 2: Using Median
Median class = 40–50
l = 40, h = 10
c.f. before median class = 3 + 7 + a = 10 + a
Median formula:
48.25 = 40 + (75 – (10 + a)) / b × 10
Simplifying:
65 – a = 0.825b
⇒ 2600 – 40a = 33b …(2)
Step 3: Using Mode
Modal class = 40–50
Mode formula:
44 = 40 + (b – a) / (2b – a – c) × 10
Simplifying:
b + 2c = 3a
⇒ 5a + b = 200 …(3)
Step 4: Solving Equations
From (3):
b = 200 – 5a
Substitute in (1):
c = 100 – a – b
Substitute values in (2):
2600 – 40a = 33(200 – 5a)
2600 – 40a = 6600 – 165a
125a = 4000
⇒ a = 32
Now,
b = 200 – 5a = 200 – 160 = 40
c = 100 – 32 – 40 = 28
Final Missing Frequencies
30–40 = 32
40–50 = 40
50–60 = 28
Class Interval : Frequency
10–20 : 3
20–30 : 7
30–40 : 32
40–50 : 40
50–60 : 28
60–70 : 20
70–80 : 16
80–90 : 4
Total : 150
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👉 Note Important questions of Business Statistics.
Three Missing Frequency
Three Missing Frequency