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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

#### 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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