Question

the median of observations 11, 12, 14, 18, x + 2, 20, 22, 25, 61 arrange in descending order is 21. find the value of x

Answer 1

Answer:

$\red { Value \: of \: x } \green {= 19}$

Step-by-step explanation:

$Given \: observations \: 11,12,13,18,(x+2),20,\\25,\:61$

/* Arranging in descending order, we get

$61,\:25,\:22,\:20,\:(x+2),\:18,\:13,\:12,\:11$

$Number \: of \: observations \pink{(n) }= 9\:(Odd)$

$Median = \left( \frac{n+1}{2}\right)^{th} \:term$

$= \left( \frac{9+1}{2}\right)^{th} \: term$

$= \left(\frac{10}{2} \right)^{th} \: observation$

$= 5^{th} \: observation$

$= x + 2\: ---(1)$

$Median = 21 \: ---(2) \: ( Given )$

$x + 2 = 21$

$\implies x = 21 - 2$

$\implies \green { x = 19}$

Therefore.,

$\red { Value \: of \: x } \green {= 19}$

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