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Question

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 (in units)
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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Solution

Monthly consumption (in units)
Number of consumers fi
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 n2=34
So, we have the median class (125-145)
l=125,n=68,f=20,cf=22,h=20
Median=l+{n2cff}×h
=125+{342220}×20=137units.

(ii) Modal class is (25-145) having maximum frequency fm=20,f)113,f2=14,l=125 and h=20

Mode=l+{fmf12fmf1f2}×h
=125+{2013401314}×20=125+7×2013
=125+14013=125+10.76=135.76units

(iii) n=68,a=135,h=20 and fiui=7

Monthly consumption (in units)
Number of consumers
Class mark xi
ui=xi13520
fi×ui
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 fiui=7
By step-deviation method.
Mean=a+h×1n×fiui=135+20×168×7
=135+3517=135+2.05=137.05units.

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