Question

The table given below shows the daily expenditure on food of 25 households in a locality: 

Hint:

To find the mean expenditure, use the formula: \(\frac{\sum (\text{Class mark} \times \text{Number of households})}{\text{Total number of households}}\).

Answer 1

Step 1: Calculate the class mark for each expenditure range.}
The class mark is the midpoint of the class interval. For each range, we calculate the class mark as follows: \[ \text{Class mark} = \frac{\text{Lower limit} + \text{Upper limit}}{2} \] - For 100-150: \( \frac{100 + 150}{2} = 125 \)
- For 150-200: \( \frac{150 + 200}{2} = 175 \)
- For 200-250: \( \frac{200 + 250}{2} = 225 \)
- For 250-300: \( \frac{250 + 300}{2} = 275 \)

Step 2: Multiply the class marks by the number of households.}
Now, multiply the class mark for each interval by the corresponding number of households to find the total expenditure for each class. \[ \text{Total expenditure for 100-150} = 125 \times 4 = 500 \] \[ \text{Total expenditure for 150-200} = 175 \times 6 = 1050 \] \[ \text{Total expenditure for 200-250} = 225 \times 12 = 2700 \] \[ \text{Total expenditure for 250-300} = 275 \times 3 = 825 \]
Step 3: Find the total expenditure and total number of households.}
The total expenditure is the sum of all the expenditures: \[ \text{Total expenditure} = 500 + 1050 + 2700 + 825 = 5075 \] The total number of households is: \[ \text{Total households} = 4 + 6 + 12 + 3 = 25 \]
Step 4: Calculate the mean daily expenditure.}
The mean daily expenditure is calculated by dividing the total expenditure by the total number of households: \[ \text{Mean expenditure} = \frac{\text{Total expenditure}}{\text{Total households}} = \frac{5075}{25} = 203 \] % Final Answer Final Answer:
The mean daily expenditure on food is ₹ 203.