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Mathematics

Calculate the median of the following frequency distribution:

Weight (in nearest kg)Number of students
458
465
486
509
527
544
552

Measures of Central Tendency

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Answer

Cumulative frequency distribution table :

Weight (in nearest kg)Number of studentsCumulative frequency
4588
46513 (8 + 5)
48619 (13 + 6)
50928 (19 + 9)
52735 (28 + 7)
54439 (35 + 4)
55241 (39 + 2)

Here number of observations, n = 41, which is odd.

By formula,

Median=41+12th observationMedian=422th observationMedian=21th observationMedian=Weight of 21 st student\Rightarrow \text{Median} = \dfrac{41 + 1}{2} \text{th} \text{ observation} \\[1em] \Rightarrow \text{Median} = \dfrac{42}{2} \text{th} \text{ observation} \\[1em] \Rightarrow \text{Median} = 21 \text{th} \text{ observation} \\[1em] \Rightarrow \text{Median} = \text{Weight of 21 st student}

From the above table, weight of each student from 20th to 28th are 50.

∴ Weight of 21st student = 50.

Hence, median weight = 50 kg.

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