Given below is the number of units of electricity consumed in a week in a certain locality:
Consumption (in units) | 65 - 85 | 85 - 105 | 105 - 125 | 125 - 145 | 145 - 165 | 165 - 185 | 185 - 205 |
Number of consumers | 4 | 5 | 13 | 20 | 14 | 7 | 4 |
Calculate the median.
To find median, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table.
CONSUMPTION (unit) | NUMBER OF CONSUMERS(fi) | Cf |
65 - 85 | 4 | 4 |
85 - 105 | 5 | 4 + 5 = 9 |
105 - 125 | 13 | 9 + 13 = 22 |
125 - 145 | 20 | 22 + 20 = 42 |
145 - 165 | 14 | 42 + 14 = 56 |
165 - 185 | 7 | 56 + 7 = 63 |
185 - 205 | 4 | 63 + 4 = 67 |
TOTAL | 67 |
So, N = 67
⇒ N/2 = 67/2 = 33.5
The cumulative frequency just greater than (N/2 = ) 33.5 is 42, so the corresponding median class is 125 - 145 and accordingly we get Cf = 22(cumulative frequency before the median class).
Now, since median class is 125 - 145.
∴ l = 125, h = 20, f = 20, N/2 = 33.5 and Cf = 22
Median is given by,
⇒ 
= 125 + 11.5
= 136.5
Thus, median is 136.5.