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ICSE Class X Math 2013 Paper

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Question : 3 of 46
Marks: +1, -0
The median of the following observations 11, 12,14,(x−2),(x+4),(x+9),12,14,(x-2),(x+4),(x+9), 32,38,4732,38,47 arranged in ascending order is 24 . Find the value of xx and hence find the mean.
Solution:  
Given : 11,12,14,(x−2),(x+4),(x+9),3211,12,14,(x-2),(x+4),(x+9),32 , 38,47 and median =24=24 .
∵  n=9  (odd)  \because\; n=9 \;\text{(odd)}\;
∴      Median    =  n+12  th term  \therefore\;\; \;\text{Median}\;\;=\;\frac{n+1}{2} \;\text{th term}\;
  =  9+12  th term  \;=\;\frac{9+1}{2} \;\text{th term}\;
  24  =5  th term  \;24\;=5 \;\text{th term}\;
∴    x+4  =24\therefore\;\; x+4\;=24
x  =24−4x\;=24-4
x  =20x\;=20
Therefore ,11,12,14,(20−2),(20+4),, 11, 12, 14, (20-2), (20+4), (20+9),  32,38,47(20+9),\;32,38,47
  =11,12,14,18,24,29,32,38,47\;=11,12,14,18,24,29,32,38,47
    Now        Mean  =  Σxn\;\;\text{Now}\; \;\; \;\text{Mean}\;=\;\frac{\Sigma x}{n}
=    11+12+14+18+24+29+32+38+479=\;\;\frac{11+12+14+18+24+29+32+38+47}{9}
=    2259=25.=\;\;\frac{225}{9}=25.
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