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Mathematics

The weights (in kg) of 10 students of a class are given below :

21, 28.5, 20.5, 24, 25.5, 22, 27.5, 28, 21 and 24. Find the median of their weights.

Measures of Central Tendency

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Answer

Arranging the given data in ascending order:

20.5, 21, 21, 22, 24, 24, 25.5, 27.5, 28, 28.5

Here, n = 10, which is even.

By formula,

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

=102th term+(102+1) th term2=5 th term+6 th term2=24+242=482=24.= \dfrac{\dfrac{10}{2} \text{th term} + \Big(\dfrac{10}{2} + 1\Big)\text{ th term}}{2} \\[1em] = \dfrac{5\text{ th term} + 6\text{ th term}}{2} \\[1em] = \dfrac{24 + 24}{2} \\[1em] = \dfrac{48}{2} \\[1em] = 24.

Hence, median = 24.

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