Question

Following 12 observations are arranged in
ascending order as follows: 86, 90, 92, 97, 98,
5x + 4, 6x - 4, 120, 128, 149, 150, 157. If the
median of the data is 132, find the value of x.
Please

Answer 1

$\large{\pmb{\sf{\underline{Given\:Question\::}}}}$

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Following 12 observations are arranged in ascending order as follows:

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》86, 90, 92, 97, 98, 5x + 4, 6x - 4, 120, 128, 149, 150, 157.

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Median of the given data is 132.

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$\large{\pmb{\sf{\underline{Need\:to\:Find\::}}}}$

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Value of x?

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We have,

n = Number of observations: 12 (an even number)

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So, As we know that,

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¤ Formula to find Median for an ( n = even number ) is,

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$\star\:{\underline{\boxed{\frak{\purple{Median = \dfrac{\bigg( \frac{n}{2} \bigg)^{th} + \bigg( \frac{n}{2} + 1 \bigg)^{th}\:observation}{2}}}}}}$

$\bf{\dag}\:{\underline{\frak{Now,\:Putting\: Given\: values\: in\: formula,}}}$

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$:\implies\sf 132 = \dfrac{\bigg( \cancel{\frac{12}{2}} \bigg)^{th} + \bigg( \cancel{\frac{12}{2}} + 1 \bigg)^{th}\:observation}{2}\\\\\\ :\implies\sf 132 = \dfrac{6^{th} + 7^{th}\:observation}{2}\\\\\\ :\implies\sf 132 = \dfrac{(5x + 4) + (6x - 4)}{2}\\\\\\ :\implies\sf 132 = \dfrac{5x + 6x + 4 - 4}{2}\\\\\\ :\implies\sf 132 = \dfrac{5x + 6x}{2}\\\\\\ :\implies\sf 132 = \dfrac{11x}{2}\\\\\\ :\implies\sf 132 \times 2 = 11x\\\\\\\ :\implies\sf 264 = 11x\\\\\\ :\implies\sf x = \cancel{\dfrac{264}{11}}\\\\\\ :\implies{\underline{\boxed{\frak{\pink{x = 24}}}}}\:\bigstar$

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$\qquad\therefore\:{\underline{\sf{The\:value\:of\:x\:is\:{\textsf{\textbf{24}}}.}}}$