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If the median of \(\frac{x}5\) , \(\frac{x}4\) , \(\frac{x}2\) , x and \(\frac{x}3\) , where x > 0 is 8, find the value of x. |
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Answer» Since x > 0 ∴ \(\frac{x}5\) , \(\frac{x}4\) , \(\frac{x}2\) , x and \(\frac{x}3\) all are positive. Now, arranging numbers into ascending order which is \(\frac{x}5\) , \(\frac{x}4\) , \(\frac{x}3\), \(\frac{x}2\) and x. Total number are n = 5 which is odd. ∴ The median is \(\frac{n+1}2\)th term = \(\frac{5+1}2\)th term = 3rd term. Hence, the 3rd number in sequence of ascending order of numbers is the median of given numbers. ∴ The median of numbers is \(\frac{x}3\). Given that the median of number is 8. ∴ \(\frac{x}3\) = 8 ⇒ x = 3 × 8 = 24. Hence, the value of x is 24. |
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