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What is the median for the following data given below?

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35.85

33.85

55.28

65.28

answer is B.

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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
11-21	1	1
21-31	5	6
31-41	7	13
41-51	3	16
	N = 16

From the table, we get

n = Σf = 16

\frac{n}{2} = \frac{16}{2}

\Rightarrow

\frac{n}{2} = 8

We know that,
Median

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

From the table, we get that the median class is

31 - 41

=

Lower limit of the median class

= 31

n = Σf =

Total number of frequencies

= 16

\frac{n}{2} = 8

=

Cumulative frequency of the class preceding the median class

= 6

=

Frequency of the median class

= 7

=

class width

= 10

Putting the values in the formula, we get

Median = 31 + (\frac{\frac{16}{2} - 6}{7}) \times 10

\Rightarrow

Median = 31 + (\frac{8 - 6}{7}) \times 10

\Rightarrow

Median

= 31 + 2.85

\Rightarrow

Median

= 33.85

Therefore, the median of the data is

33.85

.
Hence, the correct option is 2.

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