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In the solution to Q 15 in tbe step no 1 they have arranged x before 8 and after 5. But how did they come to know that 5

Q15. If the median of 5, 9, 11, 3, 4, x, 8 is 6, find the value of x.

Sol. Arranging in ascending order, 3, 4, 5, x, 8, 9, 11,

Here n = 7 which is odd.

$\therefore \mathrm{Median}={\frac{n+1}{2}}^{\mathrm{th}}\mathrm{term}=\frac{7+1}{2}={4}^{\mathrm{th}}\mathrm{term}=x\phantom{\rule{0ex}{0ex}}\therefore \mathrm{But}\mathrm{median}=6\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore x=6$

Here we can see that we have odd number of data , We know middle one is the median .

And given median = 6 and that is missing in given data

So, we assume that missing number '

*x*' is median of given data .

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