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Mathematics

The median class for the given distribution is :

ClassFrequency
0 - 102
10 - 204
20 - 303
30 - 405

  1. 0 - 10

  2. 10 - 20

  3. 20 - 30

  4. 30 - 40

Measures of Central Tendency

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Answer

The given class intervals are already in ascending order. We construct the cumulative frequency table as under :

ClassFrequencyCumulative frequency
0 - 1022
10 - 2046 (2 + 4)
20 - 3039 (6 + 3)
30 - 40514 (9 + 5)

Here, Cumulative frequency = 14, which is even.

By formula,

Median = n2 th observation+(n2+1) th observation2\dfrac{\dfrac{\text{n}}{2} \text{ th observation} + \Big(\dfrac{\text{n}}{2} + 1\Big) \text{ th observation}}{2}

=142 th observation+(142+1) th observation2=7 th observation+(7+1) th observation2=7 th observation+8 th observation2= \dfrac{\dfrac{14}{2} \text{ th observation} + \Big(\dfrac{14}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{7 \text{ th observation} + \Big(7 + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{7 \text{ th observation} + 8 \text{ th observation}}{2}

All observations from 7th to 9th are equal, each lies in the interval 20 - 30.

So, median class = 20 - 30

Hence, Option 3 is the correct option.

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