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.

Monthly consumption (in units)	Number of consumers
$65-85$	$4$
$85-105$	$5$
$105-125$	$13$
$125-145$	$20$
$145-165$	$14$
$165-185$	$8$
$185-205$	$4$

(N/A) $1$. Mean: Using the step deviation method,$\bar{x} = a + h \left( \frac{\sum f_i u_i}{\sum f_i} \right)$. With $a = 135, h = 20, \sum f_i u_i = 7, \sum f_i = 68$,we get $\bar{x} = 135 + 20 \left( \frac{7}{68} \right) = 135 + 2.06 = 137.06$.
$2$. Mode: Modal class is $125-145$ $(f_1=20, f_0=13, f_2=14)$. Mode $= l + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h = 125 + \left( \frac{20 - 13}{40 - 13 - 14} \right) \times 20 = 125 + \left( \frac{7}{13} \right) \times 20 = 125 + 10.77 = 135.77$.
$3$. Median: $n=68, n/2=34$. Cumulative frequency table shows median class is $125-145$. Median $= l + \left( \frac{n/2 - cf}{f} \right) \times h = 125 + \left( \frac{34 - 22}{20} \right) \times 20 = 125 + 12 = 137$. Comparing them,Mean $\approx$ Median $\approx$ Mode.