The table below shows the daily expenditure on food of 25 households in a locality.
`{:("Dail expenditure (in Rs)",100-150,150-200 , 200 - 250 , 250 -300,300-350),("Number of households",4,5,12,2,2):}`
Find the mean daily expenditure on food by suitable method.

Answer

To find the mean daily expenditure on food based on the given data, we will follow these steps:

### Step 1: Create a Frequency Table
We will create a frequency table with the given data.

| Daily Expenditure (in Rs) | Number of Households (fi) | Mid-value (xi) | fi * xi |
|----------------------------|---------------------------|----------------|---------|
| 100 - 150 | 4 | 125 | 500 |
| 150 - 200 | 5 | 175 | 875 |
| 200 - 250 | 12 | 225 | 2700 |
| 250 - 300 | 2 | 275 | 550 |
| 300 - 350 | 2 | 325 | 650 |
| **Total** | **25** | | **5275**|

### Step 2: Calculate Mid-values
The mid-value for each class interval is calculated as follows:
- For 100 - 150: (100 + 150) / 2 = 125
- For 150 - 200: (150 + 200) / 2 = 175
- For 200 - 250: (200 + 250) / 2 = 225
- For 250 - 300: (250 + 300) / 2 = 275
- For 300 - 350: (300 + 350) / 2 = 325

### Step 3: Calculate fi * xi
Now, we will calculate the product of the number of households (fi) and the mid-value (xi) for each class interval:
- For 100 - 150: 4 * 125 = 500
- For 150 - 200: 5 * 175 = 875
- For 200 - 250: 12 * 225 = 2700
- For 250 - 300: 2 * 275 = 550
- For 300 - 350: 2 * 325 = 650

### Step 4: Find the Summation of fi and Summation of fi * xi
Now we will sum up the number of households (fi) and the products (fi * xi):
- Summation of fi (n) = 4 + 5 + 12 + 2 + 2 = 25
- Summation of fi * xi = 500 + 875 + 2700 + 550 + 650 = 5275

### Step 5: Calculate the Mean
The mean daily expenditure can be calculated using the formula:
\[ \text{Mean} = \frac{\sum (fi \cdot xi)}{\sum fi} \]
Substituting the values we found:
\[ \text{Mean} = \frac{5275}{25} = 211 \]

### Conclusion
The mean daily expenditure on food by the households is **Rs. 211**.

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