The monthly expenditure on milk in 200 families of a Housing Society is given below: Find the value of x and also, find the median and mean…

Monthly Exp. (in ₹)	x	\(\displaystyle \mathrm{f}_{\mathrm{i}}\)	\(\displaystyle \mathrm{c}_{\mathrm{f}}\)	d	\(\displaystyle \mathrm{x}_{\mathrm{i}} \mathrm{f}_{\mathrm{i}}\)
$\displaystyle 1000$-$\displaystyle 1500$	$\displaystyle 1250$	$\displaystyle 24$	$\displaystyle 24$	-$\displaystyle 3$	-$\displaystyle 72$
$\displaystyle 1500$-$\displaystyle 2000$	$\displaystyle 1750$	$\displaystyle 40$	$\displaystyle 64$	-$\displaystyle 2$	-$\displaystyle 80$
$\displaystyle 2000$-$\displaystyle 2500$	$\displaystyle 2250$	$\displaystyle 33$	$\displaystyle 97$	-$\displaystyle 1$	-$\displaystyle 33$
$\displaystyle 2500$-$\displaystyle 3000$	$\displaystyle 2750$	\(\displaystyle \mathrm{x}=28\)	$\displaystyle 125$	$\displaystyle 0$	$\displaystyle 0$
$\displaystyle 3000$-$\displaystyle 3500$	$\displaystyle 3250$	$\displaystyle 30$	$\displaystyle 155$	$\displaystyle 1$	$\displaystyle 30$
$\displaystyle 3500$-$\displaystyle 4000$	$\displaystyle 3750$	$\displaystyle 22$	$\displaystyle 177$	$\displaystyle 2$	$\displaystyle 44$
$\displaystyle 4000$-$\displaystyle 4500$	$\displaystyle 4250$	$\displaystyle 16$	$\displaystyle 193$	$\displaystyle 3$	$\displaystyle 48$
$\displaystyle 4500$-$\displaystyle 5000$	$\displaystyle 4750$	$\displaystyle 7$	$\displaystyle 200$	$\displaystyle 4$	$\displaystyle 28$
Total					-$\displaystyle 35$

\(\displaystyle 172+x=200 \quad \Rightarrow x=28\) \(\displaystyle l=\) lower limit of median class \(\displaystyle =2500\) \[\frac{N}{2}=\frac{200}{2}=100 \] \(\displaystyle \mathrm{C}=97, \mathrm{f}=28, \mathrm{~h}=500\) \[\begin{aligned} \text { Median } & =l+\frac{\dfrac{\mathrm{N}}{2}-\mathrm{C}}{\mathrm{f}} \times \mathrm{h} \\ & =2500+\frac{100-97}{28} \times 500 \\ & =2500+\frac{3}{28} \times 500=2553 \cdot 6 \end{aligned} \] Median Expenditure \(\displaystyle =₹ 2553 \cdot 6\) Mean \(\displaystyle =2750-\frac{35 \times 500}{200}=2750-87 \cdot 5=2662 \cdot 5\) Mean Expenditure \(\displaystyle =₹ 2662 \cdot 5\)