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An Incomplete Distribution is Given as Follows: Variable: 0 - 10 10 - 20 20 - 30 30 - 40 40 – 50 50 - 60 60 - 70 - CBSE Class 10 - Mathematics

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Question

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.

Solution

Class interval Frequency Cumulative frequency
0 - 10 10 10
10 - 20 20 30
20 - 30 f1 30 + f1
30 - 40 40 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

The median class = 30 - 40

l = 30, h = 40 - 30 = 10, f = 40, F = 30 + f1

Median `=l+{(N/2-F)/f}xxh`

`35=30+{(85-(30 + f1))/40}xx10`

`35=30+(55-f1)/40xx10`

`35-30=(55-f1)/4`

`5=(55-f1)/4`

5 x 4 = 55 - f1

20 = 55 - f1

f1 = 55 - 20

f1 = 35

Given

Sum of frequencies = 170

⇒ 10 + 20 + f1 + 40 + f2 + 25+ 15 = 170

⇒ 10 + 20 + 35 + 40 + f2 + 25+ 15 = 170

⇒ 145 + f2 = 170

⇒ f2 = 170 - 145

⇒ f2 = 25

∴ f1 = 35 and f2 = 25

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Solution An Incomplete Distribution is Given as Follows: Variable: 0 - 10 10 - 20 20 - 30 30 - 40 40 – 50 50 - 60 60 - 70 Concept: Median of Grouped Data.
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