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What is the median of the farm size for the following data?

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12.125

8.125

7.125

6.125

answer is A.

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Detailed Solution

It is given the frequency distribution table.
Question Image

We create a cumulative frequency table for the given data.

Class Interval	Frequency(f)	Cumulative frequency
2-5	4	4
5-8	8	12
8-11	12	24
11-14	16	40
14-17	20	60
	N = 60

From the table, we get

n = Σf = 60

\frac{n}{2} = \frac{60}{2}

\Rightarrow \frac{n}{2} = 30

30th observation lies between cumulative frequencies

24

and

40

. So, the median class is

11 - 14

We know that,
Median

= l + (\frac{\frac{n}{2} - cf}{f}) \times h

=

Lower limit of the median class

= 11

=

Cumulative frequency of the class preceding the median class

= 24

=

Frequency of the median class

= 16

=

class width

= 3

Putting the values in the formula, we get

Median = 11 + (\frac{\frac{60}{2} - 24}{16}) \times 3

\Rightarrow Median

= 11 + (\frac{30 - 24}{16}) \times 3

\Rightarrow Median

= 11 + 1.125

\Rightarrow Median

= 12.125

Therefore, the median of the data is

12.125

.
Hence, the correct option is 1.

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