Mathematics

The following observations have been arranged in ascending order. If the median of the data is 78, find the value of x.
44, 47, 63, 65, x + 13, 87, 93, 99, 110.

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Number of observations, n = 9 (odd)

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

⇒ 78 = $\Big[\dfrac{9+1}{2}\Big]^{th}$ term

⇒ 78 = $\Big[\dfrac{10}{2}\Big]^{th}$ term

⇒ 78 = $5^{th}$ term

⇒ 78 = x + 13

⇒ x = 78 - 13

⇒ x = 65

Hence, the value of x is 65.

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