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What is the mode for the following frequency distribution?

Size of Items
Frequency
0-4
5
4-8
7
8-12
9
12-16
17
16-20
12
20-24
10
24-28
6
28-32
3
32-36
1
36-40
0

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32.66

14.46

14

None of these

answer is B.

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Detailed Solution

It is given the size of items and frequency.

Size of Items	Frequency
0-4	5
4-8	7
8-12	9
12-16	17
16-20	12
20-24	10
24-28	6
28-32	3
32-36	1
36-40	0

We know that,
Mode

= l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h

Where:

l \to

lower limit of the modal class

f \to

frequency of the modal class

f_{1} \to

frequency of the class preceding the modal class

f_{2} \to

frequency of the class succeeding the modal class

h \to

class width
From the given table, we get that the maximum frequency is

17

and the corresponding class is

12 - 16

.
So,

12 - 16

is the modal class.
According to the situation,

l = 12, h = 4, f = 17, f_{1} = 9

and

f_{2} = 12

Putting the values in the formula, we get
Mode

= 12 + \frac{17 - 9}{34 - 9 - 12} \times 4

\Rightarrow Mode = 12 + \frac{8}{13} \times 4

\Rightarrow Mode = 12 + \frac{32}{13}

\Rightarrow Mode = 12 + 2.46

\Rightarrow Mode = 14.46

Therefore, the mode of the given frequency distribution is

14.46

.
Hence, the correct option is 2.

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