The value of $f 1$ from the following data if its mode is 65 where frequency $6, 8, f 1$ from the following data if its mode is 65 where frequency and 12 are in ascending order is,

Class
Frequency
0-20
6
20-40
8
40-60
$f 1$
60-80
12
80-100
6
100-120
5

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answer is B.

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Detailed Solution

Given is the following data,
Mode of the given data = 65.
Modal class = 60 - 80 (class has maximum frequency).
Frequency of the modal class

f_{1} = 12

,
Class width

= h

= 100 − 80 = 20

Lower limit of the modal class = 60.
We know,

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

where,

l = Lower limit of the modal class h = Class width f 1 = Frequency of the modal class f 0 = Frequency of the class preceding the modal class f 2 = Frequency of the class succeeding the modal class

Let,
Frequency of the class preceding the modal class

f_{0} = f_{1}

=F (say)
Frequency of the class succeeding the modal class

= f_{2} = 6

.
On substituting the values, we get,
Question Image

The value of

f_{1}

=10.
Hence, option 2 is correct.

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