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ICSE Class X Math 2014 Solved Paper

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Question : 12
Total: 52
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 .
‌ Mean ‌‌=‌
6+8+10+12+13+x
6

‌=‌
49+x
6

No. of terms (n)=6 (even)
‌ Median ‌‌=‌
(
n
2
)‌th ‌‌ term ‌+(
n
2
+1)‌th ‌‌ term ‌
2

‌ Median ‌‌=‌
(
6
2
)‌th ‌‌ term ‌+(
6
2
+1)‌th ‌‌ term ‌
2

‌=‌
3‌rd ‌+4‌th ‌
2

‌=‌
10+12
2
=‌
22
2
=11
According to given condition
‌
49+x
6
‌=11
⇒‌‌49+x‌=66
x‌=17
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