Question

Given below is the number of units of electricity consumed in a week in a certain locality:
$\begin{array}{cccccccc}\text{Consumption}& 65-85& 85-105& 105-125& 125-145& 145-165& 165-185& 185-205\\ \text{(in units)}& & & & & & & \\ \text{Number of}& 4& 5& 13& 20& 14& 7& 4\\ \text{consumers}& & & & & & & \end{array}$
Calculate the median.

Answer 1

We prepare the cumulative frequency table, as shown:

Class	Frequency (f)	Cumulative frequency
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

N= 67

⇒N/2=33.5

The cumulative frequency greater than 33.5 is 42 and the corresponding class is 125-145.

Thus the median class is 125-145.

Therefore, l= 125, h = 20, f = 20,
c.f. of preceding class = 22 and N/2=33.5

Median,
M=l+((N/2−cf)/f)×h

Median=125+(33.5–22/20)×20
Median=125+11.5

Median=136.5

Hence, median is 136.5 .