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ICSE Class X Math 2015 Solved Paper

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The weight of 50 workers is given below :
 Weight in Kg  No. Workers
 50-60  4
 60-70  7
 70-80  11
 80-90  14
 90-100  6
 100-110  5
 110-120  3

Draw an ogive of the given distribution using a graph sheet. Take 2‌cm=10‌kg on one axis and 2‌cm=5 workers along the other axis. Use a graph to estimate the following :
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Question : 41
Total: 52
the upper and lower quartiles.
Solution:  
 Weight in Kg  f  cf
 50-60  4  4
 60-70  7  11
 70-80  11  22
 80-90  14  36
 90-100  6  42
 100-110  5  47
 110-120  3  50
   Σf=50  


Lower quartile (Q1)=(‌
N
4
)‌th ‌ term
‌=(‌
50
4
)th‌ term ‌
‌=12.5‌th‌ term ‌
‌=72‌kg.
Upper quartile (Q3)‌=(‌
3N
4
)th‌ term ‌
‌=(‌
150
4
)th‌ term ‌
‌=37.5‌th‌ term ‌
‌=92‌kg.
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