The graph below depicts the distribution of monthly electricity expenditure (in Rs.) by households in a specific village.

Find the median monthly electricity expenditure for households.

Monthly expenditure	150-225	225-300	300-375	375-450	450-525	525-600	600 and above
No of households	65	171	196	75	53	26	14

 

To calculate the median from the following interval data, we must first compute the cumulative frequencies.

We will use the cumulative frequency to find the median class and then apply the formula to find the median of a data set. 

Median$=l+\frac{\left(\frac{\mathrm{N}}{2}-\mathrm{cf}\right)}{{\mathrm{f}}_{\mathrm{m}}}\times \mathrm{c}$

Consider the following table, to calculate the median:

Median $=l+\frac{\left(\frac{\mathrm{N}}{2}-\mathrm{cf}\right)}{{\mathrm{f}}_{\mathrm{m}}}\times \mathrm{c}$

Here,

Class Interval c $=75$

$\text{N}=\Sigma {\text{f}}_{\text{i}}=600$

$\frac{\text{N}}{2}=300$

$\Rightarrow \text{ Median class }=300-375$

Frequency of median class $f_{\mathrm{m}}=196$

The lower limit of the median class $l = 300$

Cumulative frequency of the class before the median class $c.f.=236$

 Median $=300+\frac{\left(\frac{600}{2}-236\right)}{196}\times 75$

 Median $=300+\frac{\left(64\right)}{196}\times 75$

 Median $=324.489\approx 324.49$