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Mathematics

The marks of 15 students in an examination are given below :

17, 35, 21, 17, 19, 25, 29, 23, 24, 31, 40, 19, 22, 20, 26.

Find the median score.

Measures of Central Tendency

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Answer

By arranging data in ascending order, we get:

17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40

Number of observations, n = 15, which is odd.

By formula,

⇒Median=n+12th observation⇒Median=15+12th observation⇒Median=162th observation⇒Median=8 th observation⇒Median=23\Rightarrow \text{Median} = \dfrac{\text{n} + 1}{2} \text{th} \text{ observation} \\[1em] \Rightarrow \text{Median} = \dfrac{15 + 1}{2} \text{th} \text{ observation} \\[1em] \Rightarrow \text{Median} = \dfrac{16}{2} \text{th} \text{ observation} \\[1em] \Rightarrow \text{Median} = 8 \text{ th} \text{ observation} \\[1em] \Rightarrow \text{Median} = 23

Hence, median score = 23.

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