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Mathematics

The following data have been arranged in ascending order of magnitude.

63, 66, 69, x, x + 2, 76, 89 and 103.

If the median of the given data is 71, find the value of x.

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Answer

n = 8

Median = (n2)th term+(n2+1)th term2\dfrac{\Big(\dfrac{n}{2}\Big)^{th}\text{ term} + \Big(\dfrac{n}{2} + 1\Big)^{th}\text{ term}}{2}

Median = (82)th term+(82+1)th term2\dfrac{\Big(\dfrac{8}{2}\Big)^{th} \text{ term}+ \Big(\dfrac{8}{2} + 1\Big)^{th}\text{ term}}{2}

= 4th term+(4+1)th term2\dfrac{4^{th}\text{ term} + (4 + 1)^{th}\text{ term}}{2}

= 4th term+5th term2\dfrac{4^{th}\text{ term} + 5^{th}\text{ term}}{2}

= x+(x+2)2\dfrac{x + (x + 2)}{2}

= x+x+22\dfrac{x + x + 2}{2}

= 2x+22\dfrac{2x + 2}{2}

= x + 1

⇒ x + 1 = 71

⇒ x = 71 - 1

⇒ x = 70

Hence, the value of x is 70.

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