33. In the following distribution, locate the median,
mean and mode.
monthly no. of
consumption. consumers
of electricity
65-85. 4
85-105. 5
105-125. 13
125-145. 20
145-165. 14
165-185. 7
185-205. 4
Answers
Step-by-step explanation:
_______________________________
consumption. consumers x ui fiui cf
_______________________________
65-85. 4 75 -3 -12 4
85-105. 5 95 -2 -10 9
105-125. 13 115 -1 -13 22
125-145. 20 135 0 0 42
145-165. 14 155 1 14 56
165-185. 7 175 2 14 73
185-205. 4 195 3 12 77
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£fi=77 £fiui= 5
a= 135 h=20
mean = a + (£fiui/£fi) ×h
= 135 + 5×20/77
= 135+1.298..
mean = 136.3 approximately
n/2=77/2= 33.5
so 125-145 is median class
l= 125 cf = 22, f = 20 h= 20
median = l + [(n/2-cf)/f]× h
= 125+[33.5-22)/20]×20
=125 + 11.5
median = 136.5
highest frequency is 20
modal class 125-145
so l = 125, f0= 13, f1=20, f2=14, h =20
mode = l + [ (/f1- f0) 2f1-f2-f0)]×h
= 125+[(20-13)/(40-13-14)]×20
= 125+( 7/13)×20
125+10769..
mode = 135. 77 approximately