The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
The given data is shown below.
Here, the maximum frequency is 20 so the modal class is 125−145.
Therefore,
$l=125$
$h=20$
$f=20$
$f_{1}=13$
$f_{2}=14$
$\Rightarrow$ Mode $=l+\frac{f-f_{1}}{2 f-f_{1}-f_{2}} \times h$
$=125+\frac{7}{13} \times 20$
$=125+\frac{140}{13}$
Mode $=135.76$ units
Thus, the mode of the monthly consumption of electricity is 135.76 units.
Mean $=\frac{\sum f_{i} x_{i}}{\sum f}=\frac{9320}{68}=137.05$
Thus, the mean of the monthly consumption of electricity is 137.05 units.
Here,
Total number of consumers, $N=68$ (even)
Then, $\frac{N}{2}=34$
$\therefore$ Median
$=l+\frac{\frac{N}{2}-F}{f} \times h$
$=125+\frac{\frac{68}{2}-22}{20} \times 20$
$=125+\frac{34-22}{20} \times 20$
$=125+12$
$=137$
Thus, the median of the monthly consumption of electricity is 137 units.