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What is the mode for the grouped data?

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10.5

12.5

13.7

8.88

answer is D.

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Detailed Solution

It is given the frequency distribution table.
Question Image

From the data, we get that frequency of class interval

8 - 10

is maximum.
So, it is the modal class.
Now,

l =

lower limit of modal class

= 8

f_{1}

=

frequency of modal class

= 10

f_{0}

=

frequency of class preceding the modal class

= 6

f_{2}

=

frequency of class succeeding the modal class

= 5

h =

class interval width

= 2

So, Mode

=

l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h)

Putting the values in the formula, we get
Mode

=

8 + (\frac{10 - 6}{2 \times 10 - 6 - 5} \times 2)

\Rightarrow

Mode

= 8 + 0.88

\Rightarrow

Mode = 8.88
Thus, the mode of the data is

8.88

.
Hence, the correct option is 4.

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