An incomplete distribution is given as follows:
Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

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Solution

Class interval Frequency Cumulative frequency

0 – 10 10 10

10 – 20 20 30

20 – 30 f₁ 30 + f₁(F)

30 – 40 40 (F) 70 + f₁

40 – 50 f₂ 70 + f₁+ f₂

50 – 60 25 95 + f₁+ f₂

60 – 70 15 110 + f₁+ f₂

N = 170

Given

Median = 35

Then median class = 30 – 40

L = 30, h = 40 – 30 = 10, f = 40, F = 30 + f₁
$Median space equals space straight L plus fraction numerator begin display style straight N over 2 minus straight F end style over denominator straight f end fraction cross times straight h space space35 space equals space 30 plus fraction numerator begin display style 170 over 2 minus left parenthesis 30 plus straight f subscript 1 right parenthesis end style over denominator 40 end fraction cross times 1035 space â�� space 30 space equals space fraction numerator 85 â�� 30 â�� straight f subscript 1 over denominator 40 end fraction cross times 105 space equals space fraction numerator 55 â�� straight f over denominator 4 end fraction20 space equals space 55 space â�� space straight f subscript 1$
f₁= 55 – 20 = 35

Given

Sum of frequencies = 170

10 + 20 + f_i+ 40 + f₂+ 25 + 15 = 170

10 + 20 + 35 + 40 + f₂+ 25 + 15 = 170

f₂ = 25

f₁ = 35 and f₂=25

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Class interval	Frequency	Cumulative frequency
0 – 10	10	10
10 – 20	20	30
20 – 30	f₁	30 + f₁(F)
30 – 40	40 (F)	70 + f₁
40 – 50	f₂	70 + f₁+ f₂
50 – 60	25	95 + f₁+ f₂
60 – 70	15	110 + f₁+ f₂
	N = 170

An incomplete distribution is given as follows: Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 Frequency: 10 20 ? 40 ? 25 15 You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.

An incomplete distribution is given as follows:
Variable: 0 -10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70
Frequency: 10 20 ? 40 ? 25 15
You are given that the median value is 35 and the sum of all the frequencies is 170. Using the median formula, fill up the missing frequencies.