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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 - CBSE Class 10 - Mathematics

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Question

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: f1 5 9 12 f2 3 2 40

Solution

Class interval Frequency Cumulative frequency
0 - 10 f1 f1
10 - 20 5 5 + f1
20 - 30 9 14 + f1
30 - 40 12 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 = 30 - 40

l = 30, h = 40 - 30 = 10, f = 12 and F = 14 + f1

Median `=l+(N/2-F)/fxxh`

`rArr32.5=30+(20-(14+f1))/12xx10`

`rArr32.5-30=(20-14-f1)/12xx10`

`rArr2.5=(6-f1)/12xx10`

`rArr2.5=(6-f1)/6xx5`

⇒ 2.5 x 6 = (6 - f1) x 5

⇒ 15 = (6 - f1) x 5

⇒ 15/5 = 6 - f1

⇒ 3 = 6 - f1

⇒ f1 = 6 - 3

⇒ f1 = 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

⇒ f2 = 6

∴ f1 = 3 and f2 = 6

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Solution 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 Concept: Median of Grouped Data.
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