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ICSE Class X Math 2013 Paper

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The mark obtained by 120 students in a test are given below :
 Marks  No. of Students
 0-10  5
 10-20  9
 20-30  16
 30-40  22
 40-50  26
 50-60  18
 60-70  11
 70-80  6
 80-90  4
 90-100  3
Draw an ogive for the given distribution on a graph sheet.
Using suitable scale for ogive to estimate the following :
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Question : 41 of 46
Marks: +1, -0
The median.
Solution:  
 Marks  No. of Students (f)   CumulativeFrequency
 0-10  5  5
 10-20  9   14
 20-30  16   30
 30-40  22  52
 40-50  26  78
 50-60  18   96
 60-70  11   107
 70-80  6   113
 80-90  4  117
 90-100  3   120
   n=120  
On the graph paper, we plot the following points :
  (10,5),(20,14),(30,30),(40,52),(50,78),   \;(10,5),(20,14),(30,30),(40,52),(50,78) \text{, }\;   (60,96),(70,107),(80,113),(90,117),(100,   \;(60,96),(70,107),(80,113),(90,117),(100 \text{, }\;   120).\;120) .
 Median =  (  n2)  th    term   \text{ Median }=\; \left(\;\frac{n}{2}\right) ^{\;\text{th }\;} \text{ term }\;
  [∵n=120,   even   ]\;{[ \because n=120, \;\text{ even }\;]}
=  1202=60  th    term   =\;\frac{120}{2}=60^{\;\text{th }\;} \text{ term }\;
From the graph 60th term =42=42
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