The monthly expenditure on milk in 200 families of a Housing Society is given below : Monthly Expenditure (in ₹)…

CBSE Class 10 Maths PYQ · Statistics · Find Freuency · 5 Marks · March 2023 · Standard

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685 Marks · March 2023 · Standard
The monthly expenditure on milk in $200$ families of a Housing Society is given below :
Monthly Expenditure (in ₹) $1000-1500$ $1500-2000$ $2000-2500$ $2500-3000$ $3000-3500$ $3500-4000$ $4000-4500$ $4500-5000$
Number of families $24$ $40$ $33$ $x$ $30$ $22$ $16$ $7$
Find the value of $x$ and also, find the median and mean expenditure on milk.
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Sol. Monthly Exp. (in ₹) $x_i$ $f_i$ $c_f$ $d$ $x_i f_i$
$1000-1500$ $1250$ $24$ $24$ $-3$ $-72$
$1500-2000$ $1750$ $40$ $64$ $-2$ $-80$
$2000-2500$ $2250$ $33$ $97$ $-1$ $-33$
$2500-3000$ $2750$ $x=28$ $125$ $0$ $0$
$3000-3500$ $3250$ $30$ $155$ $1$ $30$
$3500-4000$ $3750$ $22$ $177$ $2$ $44$
$4000-4500$ $4250$ $16$ $193$ $3$ $48$
$4500-5000$ $4750$ $7$ $200$ $4$ $28$
Total $-35$
$172 + x = 200 \Rightarrow x = 28$
$l = \text{lower limit of median class} = 2500$
$\frac{N}{2} = \frac{200}{2} = 100$
$C = 97, f=28, h = 500$
Median = $l + \frac{\frac{N}{2} - C}{f} \times h$
$= 2500 + \frac{100-97}{28} \times 500$
$= 2500 + \frac{3}{28} \times 500 = 2553.6$
Median Expenditure = ₹$2553.6$
Mean = $2750 - \frac{35 \times 500}{200} = 2750 – 87.5=2662.5$
Mean Expenditure = ₹$2662.5$
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