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ICSE Class X Math 2014 Paper

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Question : 12 of 52
Marks: +1, -0
The numbers 6,8,10,12,136,8,10,12,13 and xx are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of xx.
Solution:  
Numbers in ascending order are 6,8,10,126,8,10,12 , 13,x13, x .
   Mean     =  6+8+10+12+13+x6\; \text{ Mean } \;\; = \; \frac{6+8+10+12+13+x}{6}
  =  49+x6\; = \; \frac{49+x}{6}
No. of terms (n)=6(n)=6 (even)
   Median     =  (n2)  th     term  +(n2+1)  th     term2\; \text{ Median } \;\; = \; \frac{ \left(\frac{n}{2}\right)^{\;\text{th}\;} \; \text{ term} \; + \left(\frac{n}{2}+1\right)^{\;\text{th}\;} \; \text{ term} }{2}
   Median     =  (62)  th     term  +(62+1)  th     term2\; \text{ Median } \;\; = \; \frac{ \left(\frac{6}{2}\right)^{\;\text{th}\;} \; \text{ term} \; + \left(\frac{6}{2}+1\right)^{\;\text{th}\;} \; \text{ term} }{2}
  =  3  rd  +4  th  2\; = \; \frac{3^{\;\text{rd}\;} + 4^{\;\text{th}\;}}{2}
  =  10+122=  222=11\; = \; \frac{10+12}{2} = \; \frac{22}{2} = 11
According to given condition
  49+x6  =11\; \frac{49+x}{6} \; = 11
⇒    49+x  =66\Rightarrow \;\; 49+x \; = 66
x  =17x \; = 17
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