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The Median of the Following Data is 525. Find the Missing Frequency, If It is Given that There Are 100 Observations in the Data: - CBSE Class 10 - Mathematics

Question

The median of the following data is 525. Find the missing frequency, if it is given that there are 100 observations in the data:

 Class interval Frequency 0 - 100 2 100 - 200 5 200 - 300 f1 300 - 400 12 400 - 500 17 500 - 600 20 600 - 700 f2 700 - 800 9 800 - 900 7 900 - 1000 4

Solution

 Class interval Frequency Cumulative frequency 0 - 100 2 2 100 - 200 5 7 200 - 300 f1 7 + f1 300 - 400 12 19 + f1 400 - 500 17 36 + f1 500 - 600 20 56 + f1 600 - 700 f2 56 + f1 + f2 700 - 800 9 65 + f1 + f2 800 - 900 7 72 + f1 + f2 900 - 1000 4 76 + f1 + f2 N = 100

Given median = 525

Then median class = 500 - 600

l = 500, f = 20, F = 36 + f1 and h = 600 - 500 = 100

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

rArr525=500+(50-(36+f1))/20xx100

rArr525-500=(50-36-f1)/20xx100

⇒ 25 = (14 - f1) x 5

⇒ 25 = 70 - 5f1

⇒ 5f1 = 70 - 25

⇒ 5f1 = 45

⇒ f1 = 45/5 = 9

Given sum of frequencies = 100

⇒ 2 + 5 + f1 + 12 + 17 + 20 + f2 + 9 + 7 + 4 = 100

⇒ 2 + 5 + 9 + 12 + 17 + 20 + f2 + 9 + 7 + 4 = 100

⇒ 85 + f2 = 100

⇒ f2 = 100 - 85

⇒ f2 = 15

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Solution The Median of the Following Data is 525. Find the Missing Frequency, If It is Given that There Are 100 Observations in the Data: Concept: Median of Grouped Data.
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