If the median of the following data is 32.5, find the missing frequencies.
Class interval: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Total
Frequency: $f_{1}$ 5 9 12 $f_{2}$ 3 2 40

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Solution

Class interval Frequency Cumulative frequency

0 – 10 f₁ f₁

10 – 20 5 5 + f₁

20 – 30 9 14 + f₁

30 – 40 12 (f) 26 + f₁

40 – 50 f₂ 26 + f₁+ f₂

50 – 60 3 29 + f₁+ f₂

60 – 70 2 31 + f₁+ f₂

N = 40

Given

Median = 32.5

The median class = 90 – 40

L = 30, h = 40 – 30 = 10, f = 12, F = 14 + f₁

$M e d i a n = L + \frac{\frac{N}{2} - F}{f} \times h$

$=> 32.5 = 30 + \frac{20 - (14 + f_{1})}{12} \times 10$

$32.5 - 30 = \frac{20 - (14 + f_{1})}{12} \times 10$

$2.5 \times 12 = (6 - f_{1}) \times 10$

$30 = (6 - f_{1}) \times 10$

$3 = 6 - f_{1}$

$f_{1} = 3$

Given

Sum of frequencies = 40

f₁ + 5 + 9 + 12 + f₂ + 3 + 2 = 40

3 + 5 + 9 + 12 + f₂ + 3 + 2 = 40

34 + f₂= 40

f₂ = 40 – 34 = 6

f₁ = 3 and f₂ = 6

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