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Mathematics

The median of the following data is:

xf
102
203
302
403
501
  1. 30

  2. 31

  3. 35

  4. 40

Measures of Central Tendency

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Answer

Cumulative frequency distribution table is:

xfCumulative frequency
1022
2035 (2 + 3)
3027 ( 5 + 2)
40310 (7 + 3)
50111 (10 + 1)

Here, n = 11, which is odd.

By formula,

Median = n+12 th observation\dfrac{\text{n} + 1}{2} \text{ th observation}

=11+12 th observation=122 th observation=6 th observation= \dfrac{11 + 1}{2} \text{ th observation} \\[1em] = \dfrac{12}{2} \text{ th observation} \\[1em] = 6 \text{ th observation}

From table,

6th observation corresponds to 30.

∴ Median = 30

Hence, Option 1 is the correct option.

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