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ICSE Class X Math 2014 Solved 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 2‌cm=10 units on both axis).
Use the ogive to estimate the :
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Question : 45
Total: 52
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), ‌(60,76),(70,85),(80,91),(90,96),(100,100)

‌ Median ‌‌=(‌
n
2
)‌th ‌‌ term ‌
‌[∵n=100(‌ even ‌)]
‌=‌
100
2
=50‌th ‌‌ term ‌
From the graph 50‌th ‌ term =43 .
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