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Mathematics

The median of observations 10, 11, 13, 17, x + 5, 20, 22, 24 and 53 (arranged in ascending order) is 18; find the value of x.

Statistics

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Answer

Number of observations, n = 9 (odd)

Median = [n+12]th\Big[\dfrac{n+1}{2}\Big]^{th} term

⇒ 18 = [9+12]th\Big[\dfrac{9+1}{2}\Big]^{th} term

⇒ 18 = [102]th\Big[\dfrac{10}{2}\Big]^{th} term

⇒ 18 = [5]th\Big[5\Big]^{th} term

⇒ 18 = x + 5

⇒ x = 18 - 5

⇒ x = 13

Hence, the value of x is 13.

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