ICSE Class X Math 2014 Solved Paper

Question : 12 of 52

Marks: +1, -0

The numbers

6,8,10,12,13

and

x

are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of

x

Solution:

Numbers in ascending order are

6,8,10,12

13, x

\;\text " Mean "\;\;=\;{6+8+10+12+13+x}/{6}

\;=\;{49+x}/{6}

No. of terms

(n)=6

(even)

\;\text " Median "\;\;=\;{ ({n}/{2}) ^{\;\text "th "\;} \;\text " term "\;+ ({n}/{2}+1) ^{\;\text "th "\;} \;\text " term "\;}/{2}

\;\text " Median "\;\;=\;{ ({6}/{2}) ^{\;\text "th "\;} \;\text " term "\;+ ({6}/{2}+1) ^{\;\text "th "\;} \;\text " term "\;}/{2}

\;=\;{3^{\;\text "rd "\;}+4^{\;\text "th "\;}}/{2}

\;=\;{10+12}/{2}=\;{22}/{2}=11

According to given condition

\;{49+x}/{6}\;=11

⇒ \;\; 49+x\;=66

x\;=17

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