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ICSE Class X Math 2015 Paper

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The weight of 50 workers is given below :
 Weight in Kg\mathrm{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 2 cm=10 kg2\,\text{cm}=10\,\text{kg} on one axis and 2 cm=52\,\text{cm}=5 workers along the other axis. Use a graph to estimate the following :
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Question : 41 of 52
Marks: +1, -0
the upper and lower quartiles.
Solution:  
 Weight in Kg\text{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
   Î£f=50  
Lower quartile (Q1)=(  N4)  th   (Q_1) = \left(\;\frac{N}{4}\right)^{\;\text{th }\;} term
  =(  504)th   term   \;= \left(\;\frac{50}{4}\right)^{\text{th}} \;\text{ term }\;
  =12.5  th   term   \;=12.5\;\text{th}\;\text{ term }\;
  =72  kg.\;=72\;\text{kg}.
Upper quartile (Q3)  =(  3N4)th   term   (Q_3) \;= \left(\;\frac{3N}{4}\right)^{\text{th}} \;\text{ term }\;
  =(  1504)th   term   \;= \left(\;\frac{150}{4}\right)^{\text{th}} \;\text{ term }\;
  =37.5  th   term   \;=37.5\;\text{th}\;\text{ term }\;
  =92  kg.\;=92\;\text{kg}.
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