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In a school the mark distribution of $25$ students in a mathematics examination are given below. What is its mode?

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65

32

34

31

answer is A.

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Detailed Solution

It is given the mark distribution of

25

students in a mathematics examination.
Question Image

From the data, we get that frequency of class interval

60 - 70

is maximum.
So, it is the modal class.
Now, we get
The lower limit (l) of the modal class

= 60,

The class size (h)

= 10,

The frequency

(f_{1})

of modal class

= 10

,
The frequency

(f_{0})

of the class preceding the modal class

= 4

,
The frequency

(f_{2})

of the class succeeding the modal class

= 4 .

We know that,
Mode

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

Putting the values, we get

\Rightarrow Mode = 60 + (\frac{10 - 4}{(2 \times 10) - 4 - 4}) \times 10

\Rightarrow Mode = 60 + 0.5 \times 10

\Rightarrow Mode = 60 +

\Rightarrow Mode = 65

Thus, the mode of the data is 65.
Hence, the correct option is 1.

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