Question

Qus. 1. The following frequency distribution
gives the monthly consumption of electricity of
68 consumers of a locality. Find the median,
mean and mode of the data and compare them,
Monthly consumption No. of consumers
(in units)
4
65-85
85—105
105_125
125-145
145165
165—185
5
13
20
14
8
185205​

Answer 1

Answer:

Step-by-step explanation:

C.I x

i

​

f

i

​

f

i

​

x

i

​

c.f

65−85 75 4 300 4

85−105 95 5 475 9

105−125 115 13 1495 22

125−145 135 20 2700 42

145−165 155 14 2170 56

165−185 175 8 1400 64

185−205 195 4 780 68

∑f

i

​

=68 ∑f

i

​

x

i

​

=9320

⇒ Mean=

∑f

i

​

∑f

i

​

x

i

​

​

=

68

9320

​

=137.05

Now, n=68 and

2

n

​

=34

∴ Median class =125−145

We have, l=125,c.f=22,f=20 and h=20

⇒ Median=l+

f

2

n

​

−c.f

​

×h

=125+

20

34−22

​

×20

=125+12

∴ Median=137

Now, modal class =125−145

Then we have l=125,f

0

​

=13,f

1

​

=20,f

2

​

=14 and h=20

⇒ Mode=l+

2f

1

​

−f

0

​

−f

2

​

f

1

​

−f

0

​

​

×h

=125+

2×20−13−14

20−13

​

×20

=125+10.77

∴ Mode=135.77