Question

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	195-205
Number of consumers	4	5	13	20	14	7	4

Calculate the median

Answer 1

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=∑f=67

$$\begin{gathered} N=67 \\ \Rightarrow \frac{N}{2}=33.5 \\ \text{The cumulative frequency just greater than 33}\text{.5 is 42 and the corresponding class is 125-145.} \\ \text{Thus, the median class is 125-145.} \\ \mathrm{Now},l=125,h=20,f=20,cf=\text{c}\text{.f}\text{. of preceding class = 22 and}\frac{N}{2}=33.5 \\ \therefore \text{Median,}M=l+\left\{h\times \frac{\left(\frac{N}{2}-cf\right)}{f}\right\} \\ \text{=125+}\left\{20\times \frac{(33.5-22)}{20}\right\} \\ \text{=125+11}\text{.5} \\ \text{=136}\text{.5} \\ \text{Hence, median=136}\text{.5} \end{gathered}$$