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Students of a locality decided to create an awareness about 'Save Electricity.' They recorded the monthly consumption of electricity of 68 consumers of that locality. The following frequency distribution gives the monthly consumption of electricity of these consumers of that locality, then the mode of the data is,

Monthly Consumption
Number of Consumers
65-85
4
85-105
5
105-125
13
125-145
20
145-165
14
165-185
8
185-205
4

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135.77

289.75

135.32

None of the above

answer is A.

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Detailed Solution

Given frequency table is,

Monthly Consumption	Number of Consumers
65-85	4
85-105	5
105-125	13
125-145	20
145-165	14
165-185	8
185-205	4

We know,
The mode of the group data is given by ,

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

l

= Lower limit of the modal class.

f 1

=Frequency of modal class.

f 2

=Frequency of class succeeding the modal class.

f 0

=Frequency of class preceding the modal class.
h = class size.
The maximum class frequency is 20.

⇒

modal class is

125 − 145

Therefore,

M o d e = l + (f 1 − f 0 2 f 1 − f 0 − f 2) × h

Where,

l = 125, h = 20, f 1 = 20, f 0 = 13, f 2 = 14

⇒ M o d e = 125 + (20 − 13 2 × 20 − 13 − 14) × 20 ⇒ M o d e = 125 + 7 × 20 40 − 27 ⇒ M o d e = 125 + 14013 ⇒ M o d e = 125 + 10.77 ⇒ M o d e = 135.77

Therefore, the mode of the given data is 135.77.
Hence, option 1 is correct.

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