The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, can and mode of the data and compare them Monthly consumption 65-85 85-105 105-125 125-145 145-165 105-125 125-145 145-165 165-18 1183-305 Number of consumers 3 13 8
Answers
Answer:
= 137.05 Units
Step-by-step explanation:
Answer
Monthly consumption (in units)
Number of consumers f
i
Cumulative frequency
65-85
4
4
85-105
5
9
105-125
13
22
125-145
20
42
145-165
14
56
165-185
8
64
185-205
4
68
Total
n=68
n=68 gives
2
n
=34
So, we have the median class (125-145)
l=125,n=68,f=20,cf=22,h=20
Median=l+{
f
2
n
−cf
}×h
=125+{
⋅20
34−22
}×20=137units.
(ii) Modal class is (25-145) having maximum frequency f
m
=20,f)1−13,f
2
=14,l=125 and h=20
Mode=l+{
2f
m
−f
1
−f
2
f
m
−f
1
}×h
=125+{
40−13−14
20−13
}×20=125+
13
7×20
=125+
13
140
=125+10.76=135.76units
(iii) n=68,a=135,h=20 and ∑f
i
u
i
=7
Monthly consumption (in units)
Number of consumers
Class mark x
i
u
i
=
20
x
i
−135
f
i
×u
i
65-85
4
75
-3
-12
85-105
5
95
-2
-10
105-125
13
115
-1
-13
125-145
20
135=a
0
0
145-165
14
155
1
14
165-185
8
175
2
16
185-205
4
195
3
12
Total
n=68
7
n=68,a=135,h=20 and ∑f
i
u
i
=7
By step-deviation method.
Mean=a+h×
n
1
×∑f
i
u
i
=135+20×
68
1
×7
=135+
17
35
=135+2.05=137.05units.