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Mathematics

Find the median of :

63, 17, 50, 9, 25, 43, 21, 50, 14 and 34

Statistics

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Answer

On arranging the given set of data in ascending order, we get :

9, 14, 17, 21, 25, 34, 43, 50, 50, 63

Number of observations, n = 10 (even)

Median = 12[the value of(n2)th+the value of(n2+1)th]\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{n}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{n}{2} + 1\Big)^{th}\Big] term

= 12[the value of(102)th+the value of(102+1)th]\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{10}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{10}{2} + 1\Big)^{th}\Big] term

= 12[the value of(5)th+the value of(5+1)th]\dfrac{1}{2}\Big[\text{the value of} (5)^{th} + \text{the value of} (5 + 1)^{th}\Big] term

= 12[25+34]\dfrac{1}{2}\Big[25 + 34\Big]

= 12[59]\dfrac{1}{2}\Big[59\Big]

= 29.5

Hence, the median = 29.5.

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