Question

Given below is the number of units of electricity consumed in a week in a certain locality:

Class	65 – 85	85 – 105	105 – 125	125 – 145	145 – 165	165 – 185	185 – 200
Frequency	4	5	13	20	14	7	4

Calculate the median.

Answer 1

Class	Frequency (f)	Cumulative Frequency (cf)
65- 85	4	4
85 – 105	5	9
105 – 125	13	22
125 – 145	20	42
145 – 165	14	56
165 – 185	7	63
185 – 205	4	67
	N = Σ𝑓 = 67

Now, N = 67
`⇒ N/2` = 33.5.
The cumulative frequency just greater than 33.5 is 42 and the corresponding class is 125 - 145.
Thus, the median class is 125 – 145.
∴ l = 125, h = 20, f = 20, cf = c.f. of preceding class = 22 and `N/2` = 33.5.
Now,
Median, `M = l + {h×((N/2−cf)/f)}`
                   `= 125 + {20 × ((33.5 − 22)/20)}`
                    = 125 + 11.5
                    = 136.5
Hence, the median = 136.5.