The following frequency distribution gives the monthly consumption of electricity of the consumers of a locality. Find the median, mean and mode of the data and compare them.
Monthly consumption (in units): | 65-85 | 85-105 | 105-125 | 125-145 | 145-165 | 165-185 | 185-205 |
No. of consumers: | 4 | 5 | 13 | 20 | 14 | 8 | 4 |
Class interval | Mid value (x) | Frequency(f) | fx | Cumulative frequency |
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 |
total | N=68 | ∑fx=9320 |
Mean= =
We have, N= 68,
N/2 = 34
Hence, medium class =125- 145, such that
l=125, f’=20, f=22, h=20
Median = l +
Here, we may observe that maximum class frequency is 20 belonging to the class interval 125-145
So, modal class= 125-145
Lower limit, l= 125
f0=13, f2=14, f=20,h = 20
=