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The monthly expenditure on fruits in $200$ families of a Housing Society is given below. Find the value of $x$ and also find the mode and mean expenditure on fruits.
| Monthly Expenditure (in ₹) | No. of Families |
|---|---|
| 1000-1500 | 24 |
| 1500-2000 | 40 |
| 2000-2500 | 33 |
| 2500-3000 | 28 |
| 3000-3500 | $x$ |
| 3500-4000 | 22 |
| 4000-4500 | 16 |
| 4500-5000 | 7 |
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Correct Table (1/2 Mark)
$170 + x = 200 \implies x = 30$ (1/2 Mark)
$1500-2000$ is the modal class (1/2 Mark)
$\text{Mode} = 1500 + (\frac{40-24}{2\times40-24-33}) \times 500$ (1 Mark)
$= 1500 + 347.82$
$= 1847.82$ (1/2 Mark)
Hence the modal monthly expenditure is ₹$1847.82$
$\therefore \sum f_i x_i = 435000 + 3250 \times 30 = 532500$ (1 Mark)
Mean $= \frac{532500}{200} = 2662.50$ (1 Mark)
Hence the mean monthly expenditure is ₹$2662.50$
$170 + x = 200 \implies x = 30$ (1/2 Mark)
$1500-2000$ is the modal class (1/2 Mark)
$\text{Mode} = 1500 + (\frac{40-24}{2\times40-24-33}) \times 500$ (1 Mark)
$= 1500 + 347.82$
$= 1847.82$ (1/2 Mark)
Hence the modal monthly expenditure is ₹$1847.82$
$\therefore \sum f_i x_i = 435000 + 3250 \times 30 = 532500$ (1 Mark)
Mean $= \frac{532500}{200} = 2662.50$ (1 Mark)
Hence the mean monthly expenditure is ₹$2662.50$