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 |

Question

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.

Accepted Answer

Step 1: $172 + x = 200 \Rightarrow x = 28$
Step 2: Table with class mark $x_i$, $f_i$, $cf$, $d = x_i - 2750$, and $f_i d_i$:

| Monthly Exp. (₹) | $x_i$ | $f_i$ | $cf$ | $d$ | $f_i d_i$ |
|---|---|---|---|---|---|
| 1000-1500 | 1250 | 24 | 24 | $-3$ | $-72$ |
| 1500-2000 | 1750 | 40 | 64 | $-2$ | $-80$ |
| 2000-2500 | 2250 | 33 | 97 | $-1$ | $-33$ |
| 2500-3000 | 2750 | 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 | | | | | $-35$ |
Step 3: $l = 2500$ (lower limit of median class), $\frac{N}{2} = 100$, $C = 97$, $f = 28$, $h = 500$. Median $= l + \frac{\frac{N}{2} - C}{f} 	imes h = 2500 + \frac{100 - 97}{28} 	imes 500 = 2500 + \frac{3}{28} 	imes 500 = ₹2553.6$
Step 4: Mean $= 2750 + \frac{-35 	imes 500}{200} = 2750 - 87.5 = ₹2662.5$

Question

Solution