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ICSE Class X Math 2014 Paper

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The marks obtained by 100 students in a Mathematics test are given below :
 Marks  No. of Students
 0-10  3
 10-20  7
 20-30  12
 30-40  17
 40-50  23
 50-60  14
 60-70  9
 70-80  6
 80-90  5
 90-100  4
Draw an ogive for the given distribution on a graph sheet.
(Use a scale of 2 cm=102\,\mathrm{cm}=10 units on both axis).
Use the ogive to estimate the :
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Question : 45 of 52
Marks: +1, -0
median.
Solution:  
 Marks  No. of Students  Cumulative frequency (c.f.)
 0-10  3   3
 10-20  7   10
 20-30  12  22
 30-40  17   39
 40-50  23   62
 50-60  14  76
 60-70  9   85
 70-80  6   91
 80-90  5  96
 90-100  4  100
On the graph paper, we plot the following points :
(10,3),(20,10),(30,22),(40,39),(50,62),(10,3),(20,10),(30,22),(40,39),(50,62), (60,76),(70,85),(80,91),(90,96),(100,100)(60,76),(70,85),(80,91),(90,96),(100,100)
 Median =(n2)th term\text{ Median } = \left( \frac{n}{2} \right)^{\text{th}} \text{ term}
[∵n=100( even )]\left[ \because n=100(\text{ even }) \right]
=1002=50th term= \frac{100}{2} = 50^{\text{th}} \text{ term}
From the graph 50th50^{\text{th}} term =43=43 .
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