The following frequency distribution gives the monthly consumption

Asked by admin @ in Math viewed by 326 People

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

Answered by admin @


From table ( 1 ) ,

1 ) Median :

In the above distribution , n = 68

n/2 = 34

Now , 125 - 145 is the class whose

cumulative frequency 42 is greater

than ( and nearest to ) n/2 , i.e 34

Therefore ,

125 - 145 is the median class .

l = 125 , cf = 22 ; f = 20 , h = 20 , n = 68

Median ( M ) = l + [ ( n/2 - cf )/f ] × h

M = 125 + [ ( 34 - 22 )/20 ] × 20

M = 137 units

2 ) From Table ( 2 ) ,

Here the maximum class frequency is 20

The modal class is 125 - 145 .

l = 125 , f1 = 20 ; f0 = 13 ; f2 = 14 ; h = 20

mode ( Z ) = l + [(f1 - f0)/(2f1-f2-f0)] × h

Z = 125 + [ ( 20 - 13 )/(2×20-13-14)]×20

Z = 125 + ( 7/13 )× 20

Z = 125 + 140/13

z = 125 + 10.76

z = 135.76 units

3 ) From tanble ( 3 ),

mean = 137.05

From the above we observe that the

three measures are

approximately the same in the case .

I hope this helps you.

: )

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