The following frequency distribution gives the monthly consumption of electricity of68 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 85 - 105 105 - 125 125 - 145 145 - 165 165 - 185 185 – 205 | 4 5 13 20 14 8 4 |
The cumulative frequency of the table can be represented as:
Monthly consumption (in units) | Number of consumers | Cumulative frequency |
65 – 85 85 - 105 105 - 125 125 - 145 145 - 165 165 - 185 185 – 205 | 4 5 13 20 14 8 4 | 4 9 22 42 56 64 68 |
N= 68 |
N= 68
Hence,
Median class = 125-145
Cumulative frequency = 42
Lower limit, l = 125
cf = 22
f = 20
h = 20
Hence,
Median can be calculated as:
= 125 + 12
= 137
Now, mode can be calculated as:
Modal class = 125-145
l = 125
h = 20
f1 = 20
f0 = 13
f2 = 14
= 
= 125 + 10.77
= 135.77
Now, mean of the following data can be calculated as:
Class interval | fi | xi | di | ui | fiui |
065- 085 | 4 | 75 | -60 | -3 | -12 |
085-105 | 5 | 95 | -40 | -2 | -10 |
105-125 | 13 | 115 | -20 | -1 | -13 |
125-145 | 20 | 135 | 0 | 0 | 0 |
145-165 | 14 | 155 | 20 | 1 | 14 |
165-185 | 8 | 175 | 40 | 2 | 16 |
185-205 | 4 | 195 | 60 | 3 | 12 |
∑fi = 68 | ∑fiui= 7 |
= 137.05
Hence,
Mean, Median and Mode are more or less equal in this distribution.